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$8 an hour for 5 hours

$8 an hour for 5 hours
Wages = Hourly Rate * Hours Worked
Wages = $8 * 5
Wages = [B]$40[/B]

1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How o

1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How old is John right now?
If Mike will be 40 1 year from now, then he is:
40 - 1 = 39 years old today.
And if the current sum of Mike and John's age is 89, then we use j for John's age:
j + 39 = 89
[URL='https://www.mathcelebrity.com/1unk.php?num=j%2B39%3D89&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]j = 50[/B]

1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How

1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How old is Sharon right now?
If Paul will be 49 years old 1 year from now, this means today, he is 49 - 1 = 48 years old.
Let Sharon's age be s. Then from the current sum of Paul and Sharon's ages, we get:
s + 49 = 85
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B49%3D85&pl=Solve']Type this equation into our search engine[/URL], and get:
s = [B]36[/B]

24 coloring books, 60 crayons, and 84 markers can be packaged into at most how many identical packag

24 coloring books, 60 crayons, and 84 markers can be packaged into at most how many identical packages? How many of each would each package contain?
First, determine the greatest common factor (GCF) of 24, 60, and 84 using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=24&num2=60&num3=84&pl=GCF']GCF calculator[/URL].
GCF(24, 60, 84) = 12
So we have 12 identical packages.
Now, figure out how many coloring books, crayons, and markers for each package
[LIST]
[*]24/12 = 2 coloring books
[*]60/12 = 5 crayons
[*]84/12 = 7 markers
[/LIST]
[B]So we have 12 identical packages, each containing 2 coloring books, 5 crayons, and 7 markers[/B]

3 children painted a local park track of 5000m, Alex painted 70m, Dell painted 15m, and Tony painted

3 children painted a local park track of 5000m, Alex painted 70m, Dell painted 15m, and Tony painted 35m. This pattern continues to the end of the track. What percentage of the park did each child paint?
70 + 15 + 35 = 120
When we take[URL='https://www.mathcelebrity.com/modulus.php?num=5000mod120&pl=Calculate+Modulus'] 5000 divided by 120[/URL], we get:
41 remainder 80
So we have:
[LIST]
[*]Alex: 70 * 41 = 2870
[*]Dell: 15 * 41 = 615
[*]Tony: 35 * 41 = 1435
[/LIST]
Now Alex goes next, and paints the full 70. So he has:
2870 + 70 = 2940
Dell goes next, and paints the last 10
615 + 10 = 625
Now for percentages:
[LIST]
[*]Alex: 2940/5000 = [B]58.8%[/B]
[*]Dell: 625/5000 = [B]12.5%[/B]
[*]Tony: 1435/5000 = [B]28.7%[/B]
[/LIST]

36 PAGES AND IT 3/8CM THICK, WHAT IS THE THICKNESS OF 1 PAGE?

36 PAGES AND IT 3/8CM THICK, WHAT IS THE THICKNESS OF 1 PAGE?
Set up a proportion in pages to cm:
36 pages /3/8cm = 1 page/x cm
Cross multiply:
36x = 3/8
Divide each side by 36
x = 3/(8 * 36)
x = 1/(8*12)
x = [B]1/96 cm[/B]

4 balls in package. 8 packages of balls in a carton. how many balls would be in 125 cartons?

4 balls in package. 8 packages of balls in a carton. how many balls would be in 125 cartons?
We have 4 balls per package * 8 packages per carton * 125 cartons
[B]4,000 balls[/B]

54% of students got an F, 15% of students got a D, 19% of students got a B and 12% of students got a

54% of students got an F, 15% of students got a D, 19% of students got a B and 12% of students got an A. if there were 26 students, how many got an F?
First, we check our total percentages:
54% + 15% + 19% + 12% = 100% <-- Good, we have our full sample set
F Students = 54% * 26
F Students = 14.04 -->[B] 14[/B]

6 boys have a mean age of 10 years and 14 girls have a mean age of 5 work out the mean age of the 20

6 boys have a mean age of 10 years and 14 girls have a mean age of 5 work out the mean age of the 20 children
[U]Calculate Sum of boys ages:[/U]
Sum of boys ages/6 = 10
Cross multiply, and we get:
Sum of boys ages = 6 * 10
Sum of boys ages = 60
[U]Calculate Sum of girls ages:[/U]
Sum of girls ages/14 = 5
Cross multiply, and we get:
Sum of girls ages = 14 * 5
Sum of girls ages = 70
Average of 20 children is:
Average of 20 children = (Sum of boys ages + sum of girls ages)/20
Average of 20 children = (60 + 70)/20
Average of 20 children = 130/20
Average of 20 children = [B]6.5 years[/B]

6 years from now Cindy will be 25 years old. in 12 years, the sum of the ages of Cindy and Jose will

6 years from now Cindy will be 25 years old. in 12 years, the sum of the ages of Cindy and Jose will be 91. how old is Jose right now?
Let c be Cindy's age and j be Jose's age. We have:
c + 6 = 25
This means c = 19 using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B6%3D25&pl=Solve']equation calculator[/URL].
We're told in 12 years, c + j = 91.
If Cindy's age (c) is 19 right now, then in 12 years, she'll be 19 + 12 = 31.
So we have 31 + j = 91.
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=31%2Bj%3D91&pl=Solve']equation calculator[/URL], we get [B]j = 60[/B].

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their pre

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their present ages?
Let b be the boy's age and s be his sister's age. We're given two equations:
[LIST=1]
[*]b = s + 6
[*]b + 3 = 2(s + 3)
[/LIST]
Plug in (1) to (2):
(s + 6) + 3 = 2(s + 3)
s + 9 = 2s + 6
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B9%3D2s%2B6&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]s = 3[/B]
We plug s = 3 into Equation (1) to get the boy's age (b):
b = 3 + 6
[B]b = 9[/B]

A builder needs 36 nails to finish a projects. If the nails come in packages of 3, how many packages

A builder needs 36 nails to finish a projects. If the nails come in packages of 3, how many packages should the builder purchase?
Packages needed = Total Nails / Nails per package
Packages needed = 36/3
Packages needed = [B]12[/B]

A company delivered 498 packages on Monday. On Tuesday they delivered 639 and on Wednesday they deli

A company delivered 498 packages on Monday. On Tuesday they delivered 639 and on Wednesday they delivered 436. How many packages did the company deliver in all?
Add up all the packages:
498 + 639 + 436 = [B]1573[/B]

A delivery man had 3,456 bottles of water in his truck. The bottles were packages in cases. There we

A delivery man had 3,456 bottles of water in his truck. The bottles were packages in cases. There were 48 bottles in each case. The driver delivered 192 bottles to a store. How many cases were in the truck after delivery?
Total cases in the truck before delivery
3,456/48 = 72 cases
Driver delivers 192 bottles to the store.
192 bottles / 48 bottles per case = 4 cases
72 cases before delivery - 4 cases for delivery = 68 cases after delivery

A father is K years old and his son is M years younger. The sum of their ages is 53.

A father is K years old and his son is M years younger. The sum of their ages is 53.
Father's Age = K
Son's Age = K - M
and we know K + (K - M) = 53
Combine like terms:
2K - M = 53
Add M to each side:
2K - M + M = 53 + M
Cancel the M's on the left side, we get:
2K = 53+ M
Divide each side by 2:
2K/2 = (53 + M)/2
Cancel the 2's on the left side:
K = [B](53 + M)/2[/B]

A hypothetical population consists of eight individuals ages 14,15,17,20,26,27,28, and 30 years. Wh

A hypothetical population consists of eight individuals ages 14,15,17,20,26,27,28, and 30 years. What is the probability of selecting a participant who is at least 20 years old?
At least 20 means 20 or older, so our selection of individuals is:
{20, 26, 27, 28, 30}
This is 5 out of a possible 8, so we have [URL='http://www.mathcelebrity.com/perc.php?num=5&den=8&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']5/8 of 0.625, which is 62.5%[/URL]

a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how o

a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how old is b
We're given 3 equations:
[LIST=1]
[*]a = b + 2
[*]b = 2c
[*]a + b + c = 42
[/LIST]
Substituting equation (2) into equation (1), we have:
a = 2c + 2
Since b = 2c, we substitute both of these into equation (3) to get:
2c + 2 + 2c + c = 42
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2B2%2B2c%2Bc%3D42&pl=Solve']type this equation into our math engine[/URL] and we get:
c = 8
Now take c = 8 and substitute it into equation (2) above:
b = 2(8)
b = [B]16[/B]

A job pays $56 for 8 hours of work. how much money does the job pay per hour

A job pays $56 for 8 hours of work. how much money does the job pay per hour
Hourly Wage = Total Wages / Total Hours Worked
$56/8 = [B]$7 per hour[/B].

a laser printer prints 9 pages per minute. how long will it take to print 288 pages?

a laser printer prints 9 pages per minute. how long will it take to print 288 pages?
288 pages / 9 pages per minute = [B]32 minutes[/B]

A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents

A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents the number of packages delivered, which of the following equations could be used to find y, the total cost of mailing packages?
Set up the cost function y = C(x)
[B]C(x) = 4.95 + 11.90x[/B]

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add the

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100
Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given:
[LIST=1]
[*]m = w + 5
[*]d = 0.5m
[*]d + m + w = 100
[/LIST]
Rearrange equation 1 in terms of w my subtracting 5 from each side:
[LIST=1]
[*]w = m - 5
[*]d = 0.5m
[*]d + m + w = 100
[/LIST]
Substitute equation (1) and equation (2) into equation (3)
0.5m + m + m - 5 = 100
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get:
m = [B]42
[/B]
Now, substitute m = 42 into equation 2 to solve for d:
d = 0.5(42)
d = [B]21
[/B]
Now substitute m = 42 into equation 1 to solve for w:
w = 42 - 5
w = [B]37
[/B]
To summarize our ages:
[LIST]
[*]Man (m) = 42 years old
[*]Daughter (d) = 21 years old
[*]Wife (w) = 37 years old
[/LIST]

A man is four time as old as his son. How old is the man if the sum of their ages is 60?

A man is four time as old as his son. How old is the man if the sum of their ages is 60?
Let the son's age be a. Then the man's age is 4a.
If the sum of their ages is 60, we have:
a + 4a = 60
To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B4a%3D60&pl=Solve']type it in our math engine[/URL] and we get:
a = 12
Therefore, the man's age is:
4(12) = [B]48[/B]

A man is four times as old as his son. In five years time he will be three times as old. Find their

A man is four times as old as his son. In five years time he will be three times as old. Find their present ages.
Let the man's age be m, and the son's age be s. We have:
[LIST=1]
[*]m = 4s
[*]m + 5 = 3(s + 5)
[/LIST]
Substitute (1) into (2)
4s + 5 = 3s + 15
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D3s%2B15&pl=Solve']equation calculator[/URL], and we get [B]s = 10[/B].
m = 4(10)
[B]m = 40[/B]

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Writ

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Write two equivalent expressions for the total cost of 9 accessory package. Then find the cost.
Let c be the number of cleats, s be the number of shin guards, and b be the number of balls. We have the following cost function for 9 accessory packages:
[B]9(25c + 14s + 12b)[/B]
But if we multiply through, we get an equivalent expression:
[B]225c + 126s + 108b[/B]

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?
Let m be the number of minutes it takes to print 2,000 pages. We have the equation:
25m = 2000
[URL='https://www.mathcelebrity.com/1unk.php?num=25m%3D2000&pl=Solve']Type this equation into our search engine[/URL], and we get:
m = 80

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.
Declare variables:
[LIST]
[*]Let f be the father's age
[*]Let s be the son's age
[/LIST]
We're given two equations:
[LIST=1]
[*]s = f/4
[*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I]
[/LIST]
Using substitution, we substitute equaiton (1) into equation (2) for s:
f - f/4 = 30
To remove the denominator/fraction, we multiply both sides of the equation by 4:
4f - 4f/4 = 30 *4
4f - f = 120
3f = 120
To solve for f, we divide each side of the equation by 3:
3f/3 = 120/3
Cancel the 3's on the left side and we get:
f = [B]40[/B]

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text message

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text messages.
We set up the cost function C(x) where x is the number of text messages per month:
C(x) = Cost per text * x + Monthly cost
Plugging in our given numbers, we get:
[B]C(x) = 0.28x + 7[/B]

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?
Let the woman's age be w.
Let the mother's age be m.
We're given two equations:
[LIST=1]
[*]w = m/2
[*]m + w = 75
[/LIST]
Substitute equation (1) into equation (2) for w:
m + m/2 = 75
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2F2%3D75&pl=Solve']type this equation into our search engine [/URL]and we get:
m = [B]50
[/B]
To solve for w, we plug m = 50 into equation (1):
w = 50/2
w = [B]25[/B]

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in x number of pages, determine a function model that will represent the accumulated writing hours to finish his novel
if 3 pages = 5 hours, then we divide each side by 3 to get:
1 page = 5/3 hours per page
So x pages takes:
5x/3 hours
Our function for number of pages x is:
[B]f(x) = 5x/3[/B]

Age Difference

Determines the ages for an age difference word problem.

Age now problems

A father is three times as old as the son, and the daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63
Find the present age of the father

Ages are consecutive integers. The sum of ages are 111. What are the ages

Ages are consecutive integers. The sum of ages are 111. What are the ages
In the search engine, we type [I][URL='http://www.mathcelebrity.com/consecintwp.php?num=111&pl=Sum']sum of 2 consecutive integers is 111[/URL][/I].
We get [B]55 and 56[/B].

Alice is a machinist in a shirt factory. For the first 180 shirts she is paid $2.20 and then $2.90 p

Alice is a machinist in a shirt factory. For the first 180 shirts she is paid $2.20 and then $2.90 per garment thereafter. What are her gross wages for a week in which she produces 240 shirts?
Calculate commission on the first 180 shirts (Commission 1):
Commission 1 = Shirts (up to 180) * $2.20
Commission 1 = 180 * $2.20
Commission 1 = $396
Calculate commission on the rest of the shirts about 180 (Commission 2):
Commission 2 = Shirts Above 180 * $2.90
Commission 2 = (240 - 180) * $2.90
Commission 2 = 60 * $2.90
Commission 2 = $174
Calculate Total Commission:
Total Commission = Commission 1 + Commission 2
Total Commission = $396 + $174
Total Commission = [B]$570[/B]

Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age?

Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age?
Let a be Alvin's age and e be Elga's age. We have the following equations:
[LIST=1]
[*]a = e - 12
[*]a + e = 60
[/LIST]
Plugging in (1) to (2), we get:
(e - 12) + e = 60
Grouping like terms:
2e - 12 = 60
Add 12 to each side:
2e = 72
Divide each side by 2
[B]e = 36[/B]

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute?
Set up a proportion of pages to minutes. Since 30 minutes is a half hour, we have the number of pages (p) for 1 minute as:
90/30 = p/1
To solve this proportion for p, [URL='https://www.mathcelebrity.com/prop.php?num1=90&num2=p&den1=30&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
p = [B]3[/B]

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Ke

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software package costs $25. If their total cost is $155, what is the cost of one month of game play.
Let s be the cost of software packages and m be the months of game play. We have:
[LIST]
[*]Angie: 2s + 4m
[*]Kenny: s + m
[/LIST]
We are given each software package costs $25. So the revised equations above become:
[LIST]
[*]Angie: 2(25) + 4m = 50 + 4m
[*]Kenny: 25 + m
[/LIST]
Finally, we are told their combined cost is 155. So we add Angie and Kenny's costs together:
4m + 50 + 25 + m = 155
Combine like terms:
5m + 75 = 155
[URL='http://www.mathcelebrity.com/1unk.php?num=5m%2B75%3D155&pl=Solve']Typing this into our search engine[/URL], we get [B]m = 16[/B]

Anita read 150 pages in 5 hours. What is her reading rate in pages per minute?

Anita read 150 pages in 5 hours. What is her reading rate in pages per minute?
150 pages / 5 hours
Divide top and bottom by 5:
150/5 = 30
5/5 = 1
So we have 30 pages per hour
And 1 hour is 60 minutes, so we have:
(30 pages / 1 hour) * (1 hour / 60 minutes)
30 pages / 60 minutes
[B]0.5 pages per minute[/B]

Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages?

Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages?
Let Arvin's age be a. Let Cory's age be c. We're given two equations:
[LIST=1]
[*]a = 2c
[*]a + c = 42
[/LIST]
Plug equation (1) into equation (2):
2c + c = 42
[URL='https://www.mathcelebrity.com/1unk.php?num=2c%2Bc%3D42&pl=Solve']Plug this into our search engine[/URL] and we get:
[B]c = 14[/B]
Now, we plug c = 14 into equation 1 to solve for a:
a = 2(14)
[B]a = 28[/B]

Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age?

Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age?
Let Ashley's age be a.
Let John's age be j.
We have two equations:
[LIST=1]
[*]a = 2j
[*]a + j = 63
[/LIST]
Now substitute (1) into (2)
(2j) + j = 63
Combine like terms:
3j = 63
[URL='http://www.mathcelebrity.com/1unk.php?num=3j%3D63&pl=Solve']Typing 3j = 63 into our search engine[/URL], we get
[B]j = 21[/B]

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is each now?
Let b = Beth's age
Let c = Celeste's age
We are given:
[LIST=1]
[*]b = c - 5
[*]b + 1 + c + 1 = 57
[/LIST]
Substitute (1) into (2)
(c - 5) + 1 + c + 1 = 57
Group like terms:
2c - 3 = 57
[URL='https://www.mathcelebrity.com/1unk.php?num=2c-3%3D57&pl=Solve']Type 2c - 3 = 57 into our search engine[/URL], we get [B]c = 30[/B]
Substitute c = 30 into Equation (1), we get:
b = 30 - 5
[B]b = 25
[/B]
Therefore, Beth is 25 and Celeste is 30.

Blake and Tatsu are each assigned a paper for a class they share. Blake decides to write 4 pages at

Blake and Tatsu are each assigned a paper for a class they share. Blake decides to write 4 pages at a time while Tatsu decides to write 7 pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had?
We want the least common multiple of 4 and 7, written as LCM(4, 7). Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=7&num3=&pl=LCM']LCM Calculator[/URL], we get:
LCM(4, 7) = [B]28 pages[/B]

Blake writes 4 pages per hour. How many hours will Blake have to spend writing this week in order to

Blake writes 4 pages per hour. How many hours will Blake have to spend writing this week in order to have written a total of 16 pages?
[U]Let x = the number of hours Blake needs to write[/U]
4 pages per hour * x hours = 16
[U]Divide each side by 4[/U]
[B]x = 4 hours[/B]

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages
Our equation for this is found by multiplying pages per day times number of days;
4x = 28
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D28&pl=Solve']we type the equation into our search engine[/URL] and we get:
x = [B]7[/B]

Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry?

Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry?
Let Bob's age be b. Let Henry's age be h. We're given two equations:
[LIST=1]
[*]b = 2h
[*]b + h = 42
[/LIST]
Substitute b = 2h in equation 1 into equation 2 for b:
2h + h = 42
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2Bh%3D42&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]14[/B]

Brian's age is 3/4 of Marcus'. The sum of their ages is 14. How old are Marcus and Brian?

Brian's age is 3/4 of Marcus'. The sum of their ages is 14. How old are Marcus and Brian?
Let Marcus's age be m.
Then Brian's age = 3/4m
The sum is:
m + 3m/4 = 14
Combine like terms
7m/4 = 14
Cross multiply:
7m = 56
[URL='http://www.mathcelebrity.com/1unk.php?num=7m%3D56&pl=Solve']Plugging this into the search engine[/URL], we get m = 8.
So Brian's age = 3(8)/4 = 24/4 = 6

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations.
Let Cam's age be c. Let Lara's age be l. We're given two equations:
[LIST=1]
[*]c = l + 3 <-- older means we add
[*]c + l = 63 <-- combined ages mean we add
[/LIST]
Substitute equation (1) into equation (2):
l + 3 + l = 63
Combine like terms to simplify our equation:
2l + 3 = 63
To solve for l, [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D63&pl=Solve']we type this equation into our search engine[/URL] and we get:
l = [B]30[/B]
Now, we plug l = 30 into equation (1) to solve for c:
c = 30 + 3
c = [B]33[/B]

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations.
Let Cam's age be c.
Let Lara's age be l.
We're given two equations:
[LIST=1]
[*]c = l + 3 (Since older means we add)
[*]c + l = 63
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for c:
l + 3 + l = 63
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B3%2Bl%3D63&pl=Solve']type it in our search engine [/URL]and we get:
l = [B]30
[/B]
Now, we take l = 30 and substitute it in equation (1) to solve for c:
c = 30 + 3
c = [B]33[/B]

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Let m be the number of months. We have the pages written function P(m) as:
P(m) = 12m + 35
The problem asks for P(5):
P(5) = 12(5) + 35
P(5) = 60 + 35
P(5) = [B]95[/B]

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month unti

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Set up the equation where m is the number of months:
pages per month * m + pages written already
12m + 35
The problems asks for m = 5:
12(5) + 35
60 + 35
[B]95 pages[/B]

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse i

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them?
Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age
[LIST=1]
[*]a = c + 5
[*]j = a + 6
[*]a + c + j = 31
[*]Rearrange (1) in terms of c: c = a - 5
[/LIST]
[U]Plug in (4) and (2) into (3)[/U]
a + (a - 5) + (a + 6) = 31
[U]Combine like terms:[/U]
3a + 1 = 31
[U]Subtract 1 from each side[/U]
3a = 30
[U]Divide each side by 3[/U]
[B]a = 10[/B]
[U]Plug in 1 = 10 into Equation (4)[/U]
c = 10 - 5
[B]c = 5[/B]
Now plug 1 = 10 into equation (2)
j = 10 + 6
[B]j = 16[/B]

Dad is (y) years old. Mom is 5 years younger than Dad. What is the total of their ages

Dad is (y) years old. Mom is 5 years younger than Dad. What is the total of their ages
Dad's age:
y
Mom's age (younger means we subtract):
y - 5
The total of their ages is found by adding them together:
y + y - 5
Group like terms, and we get:
[B]2y - 5[/B]

Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, ho

Dedra took a total of 6 pages of notes during 2 hours of class. After attending 3 hours of class, how many total pages of notes will Dedra have in her notebook?
Set up a proportion of pages of notes to hours of class where p equals the number of pages of notes Dedra takes for 3 hours of class:
6/2 = p/3
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=p&den1=2&den2=3&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
p = [B]9[/B]

devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage

devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage
Let d be Devaughn's age. Let s be Sydney's age. We have two equations:
[LIST=1]
[*]d = 2s
[*]d + s = 78
[/LIST]
Substitute (1) into (2)
2s + s = 78
3s = 78
Entering [URL='http://www.mathcelebrity.com/1unk.php?num=3s%3D78&pl=Solve']3x = 78 into the search engine[/URL], we get [B]s = 26[/B].

Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take he

Deyjiana reads 30 pages in 25 minutes. If she reads 210 pages at this rate, how long will it take her?
Set up a proportion of pages to minutes, were m is the number of minutes it takes to read 210 pages:
30/25 = 210/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=30&num2=210&den1=25&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
m = [B]175[/B]

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.

Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.
Let d be Dina's age. Let a be Andrea's age. We're given:
[LIST=1]
[*]d = 2a <-- Twice means multiply by 2
[*]a + d = 72
[/LIST]
Substitute equation (1) into equation (2):
a + 2a = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B2a%3D72&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]a = 24[/B]
Substitute a = 24 into equation (1):
d = 2(24)
[B]d = 48
So Andrea is 24 years old and Dina is 48 years old[/B]

Eighty percent of the employees at Rowan University have their biweekly Wages deposit directly to th

Eighty percent of the employees at Rowan University have their biweekly Wages deposit directly to their bank by electronic deposit program. Suppose we select a random samples of 8 employees. What is the probability that three of the eight (8) sampled employees use direct deposit program?
Use the [I]binomial distribution[/I]
[LIST]
[*]p = 0.8
[*]n = 8
[*]k = 3
[/LIST]
So we want P(X = 3)
Using our [URL='http://www.mathcelebrity.com/binomial.php?n=+8&p=+0.8&k=+3&t=+5&pl=P%28X+=+k%29']binomial distribution calculator[/URL], we get P(X = 3) = [B]0.0092[/B]

Ellen reads 23 pages in 40 minutes. Rob reads 9 pages in 16 minutes. Who is the faster reader? Ju

Ellen reads 23 pages in 40 minutes. Rob reads 9 pages in 16 minutes. Who is the faster reader? Justify your answer.
Compare in terms of pages per minute.
Ellen = 23 pages / 40 minutes =0.575 pages per minute
Rob = 9 pages / 16 minutes = 0.5625 pages per minute
[B]Ellen reads faster.[/B]

Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30.

Emily is three years older than twice her sister Mary’s age. The sum of their ages is less than 30. What is the greatest age Mary could be?
Let e = Emily's age and m = Mary's age.
We have the equation e = 2m + 3 and the inequality e + m < 30
Substitute the equation for e into the inequality:
2m + 3 + m < 30
Add the m terms
3m + 3 < 30
Subtract 3 from each side of the inequality
3m < 27
Divide each side of the inequality by 3 to isolate m
m < 9
Therefore, the [B]greatest age[/B] Mary could be is 8, since less than 9 [U]does not include[/U] 9.

eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn?

eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn?
Let Eric's age be e. Let Shawn's age be s. We're given two equations:
[LIST=1]
[*]e = 2s
[*]e + s = 33
[/LIST]
Substitute equation (1) into equation (2) for e so we can solve for s:
2s + s = 33
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=2s%2Bs%3D33&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]11[/B]

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?

Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?
Let Faith's age be f. Let her mother's age be m. We're given:
[LIST=1]
[*]f = m/5
[*]f + m = 30
[/LIST]
Rearrange (1) by cross-multiplying:
m = 5f
Substitute this into equation (2):
f + 5f = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=f%2B5f%3D30&pl=Solve']Type this equation into our search engine[/URL] and we get:
f = [B]5[/B]

Foster is centering a photo that is 9/1/2 inches wide on a scrapbook pages that is 10 inches wide. H

Foster is centering a photo that is 9/1/2 inches wide on a scrapbook pages that is 10 inches wide. How far from each side of the pages should he put the picture? Enter your answer as a mixed number.
First, determine your margins, which is the difference between the width and photo width, divided by 2.
10 - 9 & 1/2 = 1/2
1/2 / 2 = [B]1/4[/B]

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?
So the last cousin is n years old. this means consecutive cousins are n + 2 years older than the next.
whether their ages are even or odd, we have the sum of 4 consecutive (odd|even) integers equal to 36. We [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof4consecutiveevenintegersis36&pl=Calculate']type this into our search engine[/URL] and we get the ages of:
[B]6, 8, 10, 12[/B]

Four-fifths of Kayla’s Math Notebook is filled. She has written on 48 pages. How many pages is there

Four-fifths of Kayla’s Math Notebook is filled. She has written on 48 pages. How many pages is there total in the notebook?
Let the total pages be p. WE're given:
4p/5 = 48
To solve for p, we[URL='https://www.mathcelebrity.com/prop.php?num1=4p&num2=48&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value'] type this equation into our search engine[/URL] and we get:
p = [B]60[/B]

Frank averages 1 strike for every 4 frames that he bowls. If he bowled 48 strikes in 1 season, how m

Frank averages 1 strike for every 4 frames that he bowls. If he bowled 48 strikes in 1 season, how many frames did Frank bowl?
Set up a proportion of strikes to frames:
1/4 = 48/x
Run this through our [URL='http://www.mathcelebrity.com/prop.php?num1=1&num2=48&den1=4&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL]:
x = [B]192 frames[/B]

Germaine earns $800 for 40 hours of work. What is her hourly wage?

Germaine earns $800 for 40 hours of work. What is her hourly wage?
Hourly Wage = Wages / Hours worked
Hourly Wage = $800 / 40
Hourly Wage = [B]$20[/B]

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.
[IMG]http://www.mathcelebrity.com/images/math_problem_library_129.png[/IMG]
If AB = 6 and AD = 8, by the Pythagorean theorem, we have BD = 10 from our [URL='http://www.mathcelebrity.com/pythag.php?side1input=6&side2input=8&hypinput=&pl=Solve+Missing+Side']Pythagorean Theorem[/URL] Calculator
Using that, we have another right triangle which we can use the [URL='http://www.mathcelebrity.com/pythag.php?side1input=10&side2input=24&hypinput=&pl=Solve+Missing+Side']pythagorean theorem[/URL] calculator to get [B]FD = 26[/B]

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This software declassifies anonymous website visitors. It tells you their company, what pages they view, and gathers the contact information for decision makers at the company. And I've negotiated a free, 7 day trial for you to try it out.
This software is best if you sell or deal with B2B transactions.
Enjoy this [URL='https://www.donsevcik.com/identify-anonymous-visitors']Google Analytics on Steroids[/URL].

Help Plz

There are three siblings in a family. Their ages add to 26. Let nicks age be "x". John in half of micks age and Pip is two thirds of johns age. write an equation and solve. Find each Childs age.

If 25% of 30% of x is 9, what is x?

If 25% of 30% of x is 9, what is x?
Convert percentages to decimals when multiplying:
25% = 0.25
30% = 0.3
0.25 * 0.3 * x = 9
0.075x = 9
Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.075x%3D9&pl=Solve']type this equation in[/URL] and we get:
x = [B]120
[MEDIA=youtube]5EwNxiBdLu0[/MEDIA][/B]

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes
Convert 15 minutes to seconds:
15 minutes = 60 * 15 = 900 seconds
Set up a proportion of pages read to seconds where p is the number of pages read in 900 seconds (15 minutes):
1/44 = p/900
[URL='https://www.mathcelebrity.com/prop.php?num1=1&num2=p&den1=44&den2=900&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
p = [B]20.45[/B]

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?

If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?
Let Frank's age be f. Let Willis's age be w. We're given two equations:
[LIST=1]
[*]f = 2w <-- Double means multiply by 2
[*]f + w = 42
[/LIST]
Substitute equation (1) into equation (2):
2w + w = 42
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2Bw%3D42&pl=Solve']type this equation into our search engine[/URL]. We get:
w = [B]14
[/B]
Now, take w = 14, and substitute it back into equation (1) to solve for f:
f = 2(14)
f = [B]28[/B]

If I have 48 days to finish a 337 page book how many pages a day will I have to read each day

If I have 48 days to finish a 337 page book how many pages a day will I have to read each day
337 pages / 48 days =[B] 7.02 pages per day[/B]

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take me to read 58 pgs?
Set up a proportion, of reading time to pages where m is the number of minutes it takes you to read 58 pages.
2 hours and 30 minutes is:
60(2) + 30
120 + 30
150 minutes
Our proportion is:
150/93.25 = m/58
[URL='https://www.mathcelebrity.com/prop.php?num1=150&num2=m&den1=93.25&den2=58&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]m = 93.3 minutes, or about 1 hour, 33 minutes[/B]

If the probability of an event occurring is 7%, what is the probability of an event not occurring?

If the probability of an event occurring is 7%, what is the probability of an event not occurring?
The probability of all event is 1, or 100%.
If we treat the success of an event as p, then q is 1 - p.
Using percentages, we have:
q = 100% - p
Given p = 7%, we have:
q = 100% - 7%
q = [B]93%[/B]

If you buy 5 packages of noodles at $1.48 each whats the total?

If you buy 5 packages of noodles at $1.48 each whats the total?
Total = Packages x Cost Per Package
Total = 5 x 1.48
Total = [B]$7.40[/B]

In January 2017 the cost of postage stamps increased from 47 cents to 49 cents. What was the percent

In January 2017 the cost of postage stamps increased from 47 cents to 49 cents. What was the percent of increase?
[URL='https://www.mathcelebrity.com/percentage-change-calculator.php?num=thecostofpostagestampsincreasedfrom47centsto49cents.whatwasthepercentofincrease&pl=Calculate']Using our percentage change calculator[/URL], we get:
[B]4.26% increase[/B]

Is this algebra?

Can anyone answer this equation?
You start off with 5 tickets and every 24min you get 1 extra ticket.
After you sell your first ticket you have exactly 10min to sell another ticket and so on.
How many tickets can you sell before you run out of tickets to sell?
Plz give the mathematical equation for others to know also[IMG]https://www.facebook.com/images/emoji.php/v9/f34/1/16/1f914.png[/IMG]

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour

Jack reads 90 pages of a book in six hours. What is the average number of pages he read each hour
90 pages / 6 hour = 90/6
Type [URL='https://www.mathcelebrity.com/fraction.php?frac1=90%2F6&frac2=3%2F8&pl=Simplify']90/6 in our search engine, click simplify[/URL], and we get:
[B]15 pages per hour[/B]

Jason wrote a total of 8 pages over 2 hours. How many hours will Jason have to spend writing this we

Jason wrote a total of 8 pages over 2 hours. How many hours will Jason have to spend writing this week in order to have written a total of 12 pages? Assume the relationship is directly proportional.
Set up a proportion of pages to hours
8 pages/2 hours = 12 pages/x hours
enter 8/2 = 12/x into the [URL='http://www.mathcelebrity.com/prop.php?num1=8&num2=12&den1=2&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']search engine[/URL]:
[B]x = 3[/B]

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An em

Jeff Bezos, who owns Amazon, has a net worth of approximately $143.1 billion (as of mid-2018). An employee in the Amazon distribution center earns about $13 an hour. The estimated lifespan of the employee is 71 years. If the employee worked 24 hours a day, every day of the year from the moment of his birth, how many lifespans would it take for him to earn wages equivalent to Jeff Bezos' net worth? Round the answer to the nearest whole number.
Calculate earnings per lifespan:
Earnings per lifespan = lifespan in years * Annual Earnings
Earnings per lifespan = 71 * 13 * 24 * 365 <-- (24 hours per day * 365 days per year)
Earnings per lifespan = 8,085,480
Calculate the number of lifespans needed to match Jeff Bezos earnings:
Number of lifespans = Jeff Bezos Net Worth / Earnings Per Lifespan
Number of lifespans = 143,100,000,000 / 8,085,480
Number of lifespans = [B]17,698.39 ~ 17,699[/B]

Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age

Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age
Let j be Jennifer's age
Let p be Peter's age
We're given two equations:
[LIST=1]
[*]j = 2p
[*]j - p = 15
[/LIST]
Substitute equation (1) into equation (2) for j
2p - p = 15
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p-p%3D15&pl=Solve']type this equation into our calculation engine[/URL] and we get:
p = [B]15[/B]

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82,

Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them
Let j be Jim's age, a be Alex's age, and u be June's age. We have 3 given equations:
[LIST=1]
[*]j + a + u = 82
[*]j = u + 9
[*]a = u - 8
[/LIST]
Substitute (2) and (3) into (1)
(u + 9) + (u - 8) + u = 82
Combine Like Terms:
3u + 1 = 82
[URL='https://www.mathcelebrity.com/1unk.php?num=3u%2B1%3D82&pl=Solve']Type this equation into the search engine[/URL], and we get u = 27.
The eldest (oldest) of the 3 is Jim. So we have from equation (2)
j = u + 9
j = 27 + 9
[B]j = 36[/B]

John read the first 114 pages of a novel, which was 3 pages less than 1/3

John read the first 114 pages of a novel, which was 3 pages less than 1/3
Set up the equation for the number of pages (p) in the novel
1/3p - 3 = 114
Add 3 to each side
1/3p = 117
Multiply each side by 3
[B]p = 351[/B]

John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel.

John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel.
Let n be the number of pages in the novel. We have:
1/3n - 3 = 114
Multiply each side by 3:
n - 9 = 342
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=n-9%3D342&pl=Solve']equation solver[/URL], we get [B]n = 351[/B].

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51

JP's age is twice the age of Reyna. The sum of their ages does not exceed 51
Let JP's age be j. Let Reyna's age be r. We're given two expressions:
[LIST=1]
[*]w = 2r
[*]r + w <= 51. ([I]Does not exceed means less than or equal to)[/I]
[/LIST]
We substitute (1) into (2) for w to get the inequality:
r + 2r <= 51
To solve this inequality, we type it in our search engine and we get:
[B]r <= 17[/B]

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out?
Let m be the number of messages. We have a cost function of:
C(m) = 9 + 0.1(m - 600)
We are given C(m) = 18.20
18.20 = 9 + 0.1(m - 600)
18.20 = 9 + 0.1m - 60
Combine like terms:
18.20 = 0.1m - 51
Add 51 to each side
0.1m = 69.20
Divide each side by 0.1
[B]m = 692[/B]

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. Wh

Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina?
[U]Assumptions and givens:[/U]
[LIST]
[*]Let Justin's age be j
[*]Let Martina's age be m
[*]j > m ([I]since Justin is older than Martina[/I])
[/LIST]
We're given the following equations :
[LIST=1]
[*]j - m = 22
[*]j + m = 54
[/LIST]
Since the coefficients of m are opposites, we can take a shortcut using the [I]elimination method[/I] and add equation (1) to equation (2)
(j + j) + (m - m) = 22 + 54
2j = 76
To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%3D76&pl=Solve']type this equation into our math engine[/URL] and we get:
j = 38
The question asks for Martina's age (m), so we can pick equation (1) or equation (2). Let's use equation (1):
38 - m = 22
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=38-m%3D22&pl=Solve']type it in our math engine[/URL] and we get:
m = [B]16[/B]

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.

kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.
Let k be Kate's age
Let m be Mars's age
We're given two equations:
[LIST=1]
[*]k = 2m. (Because twice means multiply by 2)
[*]k + m = 24
[/LIST]
Substitute equation (1) for k into equation (2):
2m + m = 24
T o solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D24&pl=Solve']type this equation into our math engine[/URL]:
m = [B]8
[/B]
We want to solve for k using m= 8. Substitute this into equation 1
k = 2(8)
k = [B]16
[/B]
Check our work for equation 1
16 = 2 * 8
16 = 16
Check our work for equation 2
16 + 8 ? 24
24 = 24
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Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How

Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How old are they?
Let k be Kendra's age, m be Morgan's age, and l be Lizzie's age. We're given:
[LIST=1]
[*]k = 0.5m
[*]k = l - 3
[*]k + l + m = 39
[/LIST]
Rearranging (1) by multiplying each side by 2, we have:
m = 2k
Rearranging (2) by adding 3 to each side, we have:
l = k + 3
Substituting these new values into (3), we have:
k + (k + 3) + (2k) = 39
Group like terms:
(k + k + 2k) + 3 = 39
4k + 3 = 39
[URL='https://www.mathcelebrity.com/1unk.php?num=4k%2B3%3D39&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]k = 9
[/B]
Substitute this back into (1), we have:
m = 2(9)
[B]m = 18
[/B]
Substitute this back into (2), we have:
l = (9) + 3
[B][B]l = 12[/B][/B]

Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relation

Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relationship between the time in class x and the number of pages y.
With x hours and y pages, our equation is:
[B]y = 4x [/B]

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this week in order to have written a total of 9 pages? Solve using unit rates.
6 pages per 2 hours equals 6/2 = 3 pages per hour as a unit rate
Set up equation using h hours:
3h = 9
Divide each side by 3
[B]h = 3[/B]

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read i

Leilani can read 20 pages in 2 minutes. if she can maintain this page, how many pages can she read in an hour?
We know that 1 hour is 60 minutes.
Let p be the number of pages Leilani can read in 1 hour (60 minutes)
The read rate is constant, so we can build a proportion.
20 pages /2 minutes = p/60
We can cross multiply:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
[SIZE=5][B]Solving for Numerator 2 we get:[/B][/SIZE]
Numerator 2 = Numerator 1 * Denominator 2/Denominator 1
[SIZE=5][B]Evaluating and simplifying using your input values we get:[/B][/SIZE]
p = 20 * 60/ 2
p = 1200/2
p = [B]600[/B]

Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are t

Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are their ages?
Let Lorda's age be l. Let Kate's age be k. We're given two equations:
[LIST=1]
[*]l + k = 30
[*]l - k = 6 <-- Since Lorda is older
[/LIST]
Add the 2 equations together and we eliminate k:
2l = 36
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%3D36&pl=Solve']Typing this equation into our search engine[/URL] and solving for l, we get:
l = [B]18[/B]
Now substitute l = 18 into equation 1:
18 + k = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=18%2Bk%3D30&pl=Solve']Type this equation into our search engine[/URL] and solving for k, we get:
k = [B]12[/B]

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find t

Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry.
Let m be Martha's age. Let h be Harry's age. We're given two equations:
[LIST=1]
[*]m = h + 18 [I](older means we add)[/I]
[*]h + m = 106
[/LIST]
Substitute equation (1) into equation (2) for m:
h + h + 18 = 106
To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=h%2Bh%2B18%3D106&pl=Solve']we type this equation into our search engine[/URL] and we get:
h = [B]44[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be?
Let m be Marty's age and w be Warren's age. We have two equations:
(1) m = 6w - 3
(2) m + w > 11
Plug (1) into (2)
6w - 3 + w > 11
Combine w terms
7w - 3 > 11
Add 3 to each side
7w > 14
Divide each side by 7
w > 2 which means [B]w = 3[/B] as the youngest age.

Math Written Assignment

Im sorta confused about this question?
He has decided to remove all the old sod (grass), bring in a new 4 inch layer of topsoil, install new in-ground sprinklers, and reseed the lawn. He seems to think that he'll be able to save money by hauling loads of topsoil from the store himself in his pickup truck, rather than paying for delivery, but I don't think he's right. You're going to help us settle this.
Here is (most of) the information you asked for:
[LIST]
[*]Is he redoing the whole yard or just the front?
He's redoing the whole yard
[*]How much topsoil does he need?
I'm not sure, you'll have to figure that out. Remember he's putting a new 4 inch layer down over all the area currently covered by grass in the overhead picture above.
[*]How big is the yard?
I'm not sure, but you can probably estimate it using the overhead picture.
[*]What kind of pickup truck does he drive?
A 2003 Ford F-150 XL.
[*]How much can the pickup carry?
The truck bed is 80 inches long, 69 inches wide, and 20 inches tall.
[*]How much is the delivery charge?
$30 per truckload on top of the soil cost. Each truckload can deliver up to 18 cubic yards.
[*]How much does the topsoil cost?
$18 per cubic yard (sold in 1/4 yard increments).
[*]How far is the soil store?
It is 9 miles away. It takes about 20 minutes to drive there.
[*]What gas mileage does the pickup truck get?
It averages 17 miles to the gallon.
[*]What is the current gas cost?
Assume it's $3.79/gallon.
[/LIST]
Using this information, figure out whether my neighbor will save money by picking up the soil himself. Use the results of your calculations to guide your decision: would you recommend that my neighbor pick up the soil himself, or pay for delivery?
Detail all your assumptions and calculations, and clearly write out your final conclusions.

Matilda needs at least $112 to buy an new dress. She has already saved $40. She earns $9 an hour bab

Matilda needs at least $112 to buy an new dress. She has already saved $40. She earns $9 an hour babysitting. Write and solve and inequality to find how many hours she will need to babysit to buy the dress.
Subtract remaining amount needed after savings:
112 - 40 = 72
Let h be her hourly wages for babysitting. We have the equation:
[B]9h = 72[/B]
Divide each side by 9
[B]h = 8[/B]

Max is 23 years younger than his father.Together their ages add up to 81.

Max is 23 years younger than his father.Together their ages add up to 81.
Let Max's age be m, and his fathers' age be f. We're given:
[LIST=1]
[*]m = f - 23 <-- younger means less
[*]m + f = 81
[/LIST]
Substitute Equation (1) into (2):
(f - 23) + f = 81
Combine like terms to form the equation below:
2f - 23 = 81
[URL='https://www.mathcelebrity.com/1unk.php?num=2f-23%3D81&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 52[/B]
Substitute this into Equation (1):
m = 52 - 23
[B]m = 29[/B]

Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava?

Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava?
Let Nava's age be n and Edward's age be e. We have 2 equations:
[LIST=1]
[*]n = e + 17
[*]n + e = 29
[/LIST]
Substitute (1) into (2)
(e + 17) + e = 29
Group like terms:
2e + 17 = 29
Running this equation [URL='http://www.mathcelebrity.com/1unk.php?num=2e%2B17%3D29&pl=Solve']through our search engine[/URL], we get:
e = 6
Substitute this into equation (1)
n = 6 + 17
[B]n = 23[/B]

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 comple

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 complete this equation to find his brothers age
Let b be the brother's age and s be the sister's age. We're given two equations:
[LIST=1]
[*]s =4b
[*]b + s = 20
[/LIST]
Plug (1) into (2):
b + 4b = 20
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B4b%3D20&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]b = 4[/B]

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?

Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?
Let n be Nicole's age. Let d be Donald's age. We're given two equations:
[LIST=1]
[*]n = 0.5d
[*]n + d = 72
[/LIST]
Substitute equation (1) into (2):
0.5d + d = 72
1.5d = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=1.5d%3D72&pl=Solve']Typing this equation into the search engine and solving for d[/URL], we get:
d = [B]48[/B]

ohn read the first 114 pages of a novel, which was 3 pages less than1/3 of the novel

Let p be the novel pages.
We have 1/3p - 3 = 114
Add 3 to each side
1/3p = 117
Multiply each side by 3
p = 351

Oliver earns $50 per day plus $7.50 for each package he delivers. If his paycheck for the first day

Oliver earns $50 per day plus $7.50 for each package he delivers. If his paycheck for the first day was $140, how many packages did he deliver that day?
His total earnings per day are the Flat Fee of $50 plus $7.50 per package delivered. We have:
50 + 7.50p = 140 where p = the number of packages delivered
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=50%2B7.50p%3D140&pl=Solve']equation solver[/URL], we have:
[B]p = 12[/B]

Pat starts reading at 1pm. He reads 5 pages in 15 minutes. If pat reads until 2:45 PM how many pages

Pat starts reading at 1pm. He reads 5 pages in 15 minutes. If pat reads until 2:45 PM how many pages has he read
From 1PM to 2:45 PM is 1 hour and 45 minutes. Since 1 hour is 60 minutes, Pat reads 105 minutes.
Calculate the 15 minute blocks:
Blocks = Total Minutes / 15
Blocks = 105/15
Blocks = 7
Pat reads 5 pages for every 15 minute block. So we have:
Total Pages Read = 5 pages * 7 blocks
Total Pages Read = [B]35[/B]

Paul’s age is 7 years younger than half of Marina’s age. Express their ages.

Paul’s age is 7 years younger than half of Marina’s age. Express their ages.
Assumptions:
[LIST]
[*]Let Paul's age be p
[*]Let Marina's age be m
[/LIST]
Our expression is:
[B]p = 1/2m - 7[/B]

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Let the cost of paper packages be p and the cost of staplers be s. We're given two equations:
[LIST=1]
[*]3p + 4s = 40
[*]5p + 6s = 62
[/LIST]
We have a system of equations. We can solve this three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get the same answer:
[LIST]
[*][B]p = 4[/B]
[*][B]s = 7[/B]
[/LIST]

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number
[B]
Each side adds up to 17
[IMG]https://www.mathcelebrity.com/images/triangle_sum_17.png[/IMG]
[/B]

read 34 pages a day how many pages read in 2 weeks

read 34 pages a day how many pages read in 2 weeks
2 weeks = 14 days
34 pages per day * 14 days = [B]476 pages[/B]

Reagan bought t T-shirts. The shirts came in 8 packages. Write an expression that shows how many T-s

Reagan bought t T-shirts. The shirts came in 8 packages. Write an expression that shows how many T-shirts were in each package.
T-shirts per package = number of packages / number of t-shirts per package
T-shirts per package = [B]8/t[/B]

Reuben finished reading his book in x days. each day, he read 4 pages.His book has 28 pages.

Reuben finished reading his book in x days. each day, he read 4 pages.His book has 28 pages.
x (days) = Total Pages / Pages Per Day
x = 28/4
[B]x = 7 days[/B]

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages

Richard is thrice as old as Alvin. The sum of their ages is 52 years. Find their ages.
Let r be Richard's age. And a be Alvin's age. We have:
[LIST=1]
[*]r = 3a
[*]a + r = 52
[/LIST]
Substitute (1) into (2)
a + 3a = 52
Group like terms:
4a = 52
[URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D52&pl=Solve']Typing this into the search engine[/URL], we get [B]a = 13[/B].
This means Richard is 3(13) = [B]39[/B]

Ricky reads 20 pages in 50 minutes. How many minutes does it take him to read one page

Ricky reads 20 pages in 50 minutes. How many minutes does it take him to read one page
Set up a proportion of pages per minute where m is the number of minutes to read one page:
20/50 = 1/m
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=20&num2=1&den1=50&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m = [B]2.5[/B]

Rita is mailing packages. Each small package costs her $2.80 to send. Each large package costs her

Rita is mailing packages. Each small package costs her $2.80 to send. Each large package costs her $3.40 . How much will it cost her to send 7 small packages and 5 large packages?
Total Cost = Small Package Cost * small packages + Large Package Cost * large packages
Total Cost = 2.80 * 7 + 3.40 * 5
Total Cost = 19.6 + 17
Total Cost = [B]$36.60[/B]

Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages

Roberto has taken 17 photos photos are placed on each odd number page and the newspaper has 10 pages total. The pages with photographs will have 3 or 4 photos each. How many pages has 3 photos and how many pages have 4 photos?
Odd pages are 1, 3, 5, 7, 9
17/5 = 3 with 2 remaining.
So all 5 pages have 3 photos. Then with 2 left over, 2 pages get 4 photos.
So 5 pages have [B]3 photos, and 2 pages have 2 photos[/B]
3(3) + 4(2) = 9 + 8 = 17

Sally worked for 35 hours and was paid 8 dollars per hour how much money did she earn

Sally worked for 35 hours and was paid 8 dollars per hour how much money did she earn?
Total Wages = Number of Hours Worked * Hourly Rate
Total Wages = 35 * 8
Total Wages = [B]280[/B]

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which

Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if he is the younger man.
Let Sam's age be s. Let' Jeremy's age be j. We're given:
[LIST=1]
[*]s = j + 2 <-- consecutive odd integers
[*]sj = 783
[/LIST]
Substitute (1) into (2):
(j + 2)j = 783
j^2 + 2j = 783
Subtract 783 from each side:
j^2 + 2j - 783 = 0 <-- This is the equation to find Jeremy's age.
To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=j%5E2%2B2j-783%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this quadratic equation into the search engine[/URL] and get:
j = 27, j = -29.
Since ages cannot be negative, we have:
[B]j = 27[/B]

Sharon is 17 years old. The sum of the ages of Sharon and John is 70

Sharon is 17 years old. The sum of the ages of Sharon and John is 70.
John's age is 70 - Sharon's age.
John's age is 70 - 17 = [B]53[/B]

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?

Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?
Let Sherry's age be s. Let the mom's age be m. We're given two equations:
[LIST=1]
[*]s = m - 31
[*]m + s = 61
[/LIST]
Substitute equation (1) into equation (2) for s:
m + m - 31 = 61
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm-31%3D61&pl=Solve']we type this equation into our search engine[/URL] and we get:
m = 46
Now, we plug m = 46 into equation (1) to find Sherry's age s:
s = 46 - 31
s = [B]15[/B]

Solution Mixture

Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.

SportStation.Store - #1 Sports Equipment Online Store!

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Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages

Tamara can proofread 16 pages in 8 minutes. How many minutes will it take her to proofread 108 pages
Set up a proportion of pages to minutes:
16 pages/8 minutes = 108 pages / p minutes
We want to solve for p.
Type [I][URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=108&den1=8&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']16/8 = 108/p[/URL][/I] into the search engine.
We get p = [B]54 minutes[/B]

The age of three sister are consecutive intergers the sum of their age is 45 what is their ages

The age of three sister are consecutive intergers the sum of their age is 45 what is their ages
Type this into the search engine: [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=thesumofthreeconsecutivenumbersis45&pl=Calculate']The sum of three consecutive numbers is 45[/URL].
We get [B]14, 15, 16[/B].

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.

The ages of three siblings are all consecutive integers. The sum of of their ages is 39.
Let the age of the youngest sibling be n. This means the second sibling is n + 1. This means the oldest/third sibling is n + 2.
So what we want is the[URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutiveintegersequalto39&pl=Calculate'] sum of 3 consecutive integers equal to 39[/URL]. We type this command into our search engine. We get:
n = 12. So the youngest sibling is [B]12[/B].
The next sibling is 12 + 1 = [B]13[/B]
The oldest/third sibling is 12 + 2 = [B]14[/B]

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re

The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother?
[LIST]
[*]Let the height of the family without the mom be f. Let the height of the mother be m.
[*]Averages mean we add the heights and divide by the number of people who were measured.
[/LIST]
We're given two equations:
[LIST=1]
[*](f + m)/6 = 6
[*]f/5 = 6
[/LIST]
Cross multiplying equation (2), we get:
f = 5 * 6
f = 30
Plug f = 30 into equation (1), we get:
(30 + m)/6 = 6
Cross multiplying, we get:
m + 30 = 6 * 6
m + 30 = 36
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]6[/B]
[SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38 numbers?
The average of averages is found by getting the sum of both groups of numbers and dividing by the count of numbers.
Calculate the sum of the first group of numbers S1:
Average = S1 / n1
18 = S1 / 20
S1 = 20 * 18
S1 =360
Calculate the sum of the second group of numbers S2:
Average = S2 / n2
20 = S2 / 18
S2 = 18 * 20
S2 =360
Our average of averages is found by the following:
A = (S1 + S2)/(n1 + n2)
A = (360 + 360)/(20 + 18)
A = 720/38
[B]A = 18.947[/B]

The book Shelly has 235 pages. she has read 110 pages. If she reads 25 pages from now on, how many m

The book Shelly has 235 pages. she has read 110 pages. If she reads 25 pages from now on, how many more days will it take her to complete the book?
Subtract the pages read to get the unread pages:
235 - 110 = 125 unread pages
Now figure out how many days, reading 25 pages per day, to read 125 pages
125/25 = [B]5 days[/B]

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered t

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 231 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer.
Digit, Probability
1, 0.301
2, 0.176
3, 0.125
4, 0.097
5, 0.079
6, 0.067
7, 0.058
8, 0.051
9, 0.046
[B][U]Fradulent Checks[/U][/B]
Digit, Frequency
1, 36
2, 32
3, 45
4, 20
5, 24
6, 36
7, 15
8, 16
9, 7
Complete parts (a) and (b).
(a) Using the level of significance α = 0.05, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey the Benford's Law?

Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

The holy bible contains 525 pages. A believer reads 10 pages during weekends and 15 pages during wee

The holy bible contains 525 pages. A believer reads 10 pages during weekends and 15 pages during weekdays. How long will it take him to finish reading the bible?
Take one 7 day week:
15 + 10 = 25 pages
525 pages/25 pages = [B]21 weeks[/B]

The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviati

The hourly wages of employees at Rowan have a mean wage rate of $10 per hour with a standard deviation of $1.20. What is the probability the mean hourly wage of a random sample of 36 employees will be larger than $10.50? Assume the company has a total of 1,000 employees
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=10.5&mean=10&stdev=1.2&n=36&pl=P%28X+>+Z%29']normal distribution calculator[/URL], we get P(x > 10.5) = [B]0.00621[/B]

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 yea

The mean age of 10 women in an office is 30 years old. The mean age of 10 men in an office is 29 years old. What is the mean age (nearest year) of all the people in the office?
Mean is another word for [U]average[/U].
Mean age of women = Sum of all ages women / number of women
We're told mean age of women is 30, so we have:
Sum of all ages women / 10 = 30
Cross multiply, and we get:
Sum of all ages of women = 30 * 10
Sum of all ages of women = 300
Mean age of men = Sum of all ages men / number of men
We're told mean age of men is 29, so we have:
Sum of all ages men / 10 = 29
Cross multiply, and we get:
Sum of all ages of men = 29 * 10
Sum of all ages of men = 290
[U]Calculate mean age (nearest year) of all the people in the office:[/U]
mean age of all the people in the office = Sum of all ages of people in the office (men and women) / Total number of people in the office
mean age of all the people in the office = (300 + 290) / (10 + 10)
mean age of all the people in the office = 590 / 20
mean age of all the people in the office = 29.5
The question asks for nearest year. Since this is a decimal, we round down to either 29 or up to 30.
Because the decimal is greater or equal to 0.5 (halfway), we round [U]up[/U] to [B]30[/B]

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. Wh

The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room?
Mean = Sum of Ages in Years / Number of People
32 = Sum of Ages in Years / 5
Cross multiply:
Sum of Ages in Years = 32 * 5
Sum of Ages in Years = 160
Calculate new mean after the next person enters the room.
New Mean = (Sum of Ages in Years + New person's age) / (5 + 1)
Given a new Mean of 40, we have:
40 = (160 + New person's age) / 6
Cross multiply:
New Person's Age + 160 = 40 * 6
New Person's Age + 160 = 240
Let the new person's age be n. We have:
n + 160 = 240
To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B160%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get:
n = [B]80[/B]

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. Wh

The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room?
The mean formulas is denoted as:
Mean = Sum of Ages / Total People
We're given Mean = 38 and Total People = 5, so we plug in our numbers:
28 = Sum of Ages / 5
Cross multiply, and we get:
Sum of Ages = 28 * 5
Sum of Ages = 140
One more person enters the room. The mean age is now 39. Set up our Mean formula:
Mean = Sum of Ages / Total People
With a new Mean of 39 and (5 + 1) = 6 people, we have:
39 = Sum of Ages / 6
But the new sum of Ages is the old sum of ages for 5 people plus the new age (a):
Sum of Ages = 140 + a
So we have:
29 = (140 + a)/6
Cross multiply:
140 + a = 29 * 6
140 + a = 174
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]34[/B]

The property taxes on a boat were $375. What was the tax rate if the boat was valued at $75,000?

The property taxes on a boat were $375. What was the tax rate if the boat was valued at $75,000?
Tax Rate = Tax Amount / Purchase Price
Tax Rate = 375 / 75,000
Tax Rate = 0.005
Tax Rates are generally expressed in percentages, so the percentage = 0.005 * 100 = [B]0.5%[/B].

The relief time provided by a standard dose of a popular children’s allergy medicine averages 7.9

The relief time provided by a standard dose of a popular children’s allergy medicine averages 7.9 hours with a standard deviation of 2.2 hours. Use Table 1.
a. Determine the percentage of children who experience relief for less than 6.4 hours if the relief time follows a normal distribution. (Round your answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=6.4&mean=7.9&stdev=2.2&n=1&pl=P%28X+%3C+Z%29']normal distribution calculator[/URL], we get
Answer = [B]0.25[/B]

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?

The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?
[U]Givens[/U]
[LIST]
[*]Let Mr. Adam's age be a
[*]Let Mrs. Benson's age be b
[*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract:
[/LIST]
[LIST=1]
[*]a + b = 55
[*]a - b = 3
[/LIST]
Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2:
(a + a) + (b - b) = 55 + 3
Combining like terms and simplifying, we get:
2a = 58
To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=2a%3D58&pl=Solve']type it in our search engine[/URL] and we get:
a = [B]29[/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. Ho

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now?
Let Levi's current age be l. Let Renee's current age be r. Were given two equations:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4(r - 7)
[/LIST]
Simplify equation 2 by multiplying through:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4r - 28
[/LIST]
Rearrange equation 1 to solve for r and isolate l by subtracting l from each side:
[LIST=1]
[*]r = 89 - l
[*]l - 7 = 4r - 28
[/LIST]
Now substitute equation (1) into equation (2):
l - 7 = 4(89 - l) - 28
l - 7 = 356 - 4l - 28
l - 7 = 328 - 4l
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get:
l = [B]67[/B]

Tiffany is 59 years old. The sum of the ages of Tiffany and Maria is 91. How old is Maria?

Tiffany is 59 years old. The sum of the ages of Tiffany and Maria is 91. How old is Maria?
Tiffany + Maria = 91
59 + Maria = 91
Subtract 59 from each side
Maria = 91 - 59
[B]Maria = 32[/B]

Tom and Damian are shooting free throws. If Tom makes 7 free throws in 9 attempts, and Damian makes

Tom and Damian are shooting free throws. If Tom makes 7 free throws in 9 attempts, and Damian makes 5 free throws in 6 attempts, who has the higher relative performance? Answer this by calculating and comparing the free throw percentages of Tom and Damian.
Tom makes 7/9. [URL='https://www.mathcelebrity.com/perc.php?num=7&den=9&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Using our percentage and decimal calculator[/URL], he makes 77.78% of the free throws.
Damian makes 5/6. [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+6&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=&pof2=&pl=Calculate']Using our percentage and decimal calculator[/URL], he makes 83.33% of the free throws.
[B]Damian[/B] has a better free throw percentage.

Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtra

Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill?
Let t be Tom's age., s be Sue's age, and b be Bill's age. We have the following equations:
[LIST=1]
[*]t = s + 2
[*]b = 2t
[*]s + t + b - 2 = 20
[/LIST]
Get (2) in terms of s
(2) b = 2(s + 2) <-- using (1), substitute for t
So we have (3) rewritten with substitution as:
s + (s + 2) + 2(s + 2) - 2 = 20
s + (s + 2) + 2s + 4 - 2 = 20
Group like terms:
(s + s + 2s) + (2 + 4 - 2) = 20
4s + 4 = 20
Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B4%3D20&pl=Solve']equation calculator [/URL]to get s = 4
Above, we had b = 2(s + 2)
Substituting s = 4, we get:
2(4 + 2) = 2(6) = [B]12
Bill is 12 years old[/B]

two pages that face each other in a book have a sum of 569

two pages that face each other in a book have a sum of 569
Pages that face each other are consecutive. Let the first page be p. The second page is p + 1.
Their sum is:
p + p + 1 = 569
[URL='https://www.mathcelebrity.com/1unk.php?num=p%2Bp%2B1%3D569&pl=Solve']Type this equation into our search engine to solve for p[/URL], and we get:
p = 284
This means p + 1 = 284 + 1 = 285
So the pages that face each other having a sum of 569 are:
[B]284, 285[/B]

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.

Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.
Let Victoria's age be v. And her neighbor's age be n. We're given:
[LIST=1]
[*]v = n + 4
[*]v + n <=14 <-- no more than means less than or equal to
[/LIST]
Substitute Equation (1) into Inequality (2):
(n + 4) + n <= 14
Combine like terms:
2n + 4 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B4%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
n <= 5
Substituting this into inequality (2):
v + 5 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=v%2B5%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]v <= 9[/B]

Which of the following is NOT TRUE about the distribution for averages?

Which of the following is NOT TRUE about the distribution for averages?
a. The mean, median, and mode are equal.
b. The area under the curve is one.
c. The curve never touches the x-axis.
d. The curve is skewed to the right.
Answer is d, the curve is skewed to the right
For a normal distribution:
[LIST]
[*] The area under the curve for a standard normal distribution equals 1
[*] Mean media mode are equal
[*] Never touches the x-axis since in theory, all events have some probability of occuring
[/LIST]

Word Problem Help

A man is three times as old as his son was at the time when the father was twice as old as his son will ne two years from now. Find the present ages of each person.

You get paid $8 an hour. You make $35 in tips. You make $167.00 in a week. How many hours did you wo

You get paid $8 an hour. You make $35 in tips. You make $167.00 in a week. How many hours did you work?
To figure out the hours worked, we first need the amount of hourly wages made:
Hourly Wages = Total Wages - Tips
Hourly Wages = $167 - $35
Hourly Wages = $132
Calculate Hours Worked
Hours Worked = Hourly Wages / Hourly Rate
Hourly Worked = $132 / $8
Hourly Worked = [B]16.5[/B]

you got paid $45 to babysit your nephew for 5 hours. How much did you get paid per hour?

you got paid $45 to babysit your nephew for 5 hours. How much did you get paid per hour?
Hourly Rate = Total Wages / Hours
Hourly Rate = 45/5
Hourly Rate = [B]$9[/B]

You have read 100 pages of a 250 book. You have 3 days left to finish the book. How many pages will

You have read 100 pages of a 250 book. You have 3 days left to finish the book. How many pages will you need to reach each day in order to be able to finish the book?
Calculate remaining pages to read:
Remaining Pages = 250 - 100 = 150
Now, calculate pages per day
Pages per day = Remaining Pages/Days left
Pages per day = 150/3
Pages per day = [B]50[/B]

You have read a 247 page book for a class and decide to read 18 pages a night. How many pages are le

You have read a 247 page book for a class and decide to read 18 pages a night. How many pages are left in the book if you have been reading for n nights?
Set up the remaining pages read function R(n). We have:
[B]R(n) = 247 - 18n[/B]

You rake leaves for five hours. You get paid $5.75 every hour. How much did you earn?

You rake leaves for five hours. You get paid $5.75 every hour. How much did you earn?
Total Wages = Hourly Wage * Hours Worked
Total Wages = $5.75 * 5
Total Wages = [B]$28.75[/B]

You receive $8 for raking leaves for 2 hours. What is your hourly wage?

You receive $8 for raking leaves for 2 hours. What is your hourly wage?
Hourly Wage = Total Wages / Hours Worked
Hourly Wage = $8 / 2
Hourly Wage = [B]$4[/B]

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?

You receive 9 text messages in 12 minutes. What is the rate of text messages per hour?
Set up a proportion of text messages to minutes. Remember, there are 60 minutes in an hour, so we have:
9/12 = t/60 where t is the number of text messages in 60 minutes (1 hour)
[URL='https://www.mathcelebrity.com/prop.php?num1=9&num2=t&den1=12&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this into the search engine[/URL], we get [B]t = 45[/B].

You start reading on page 342 and end on 531. How many pages did you read?

You start reading on page 342 and end on 531. How many pages did you read?
The pages read formula is:
Pages Read = End Page - Start Page + 1
Pages Read = 531 - 342 + 1
Pages Read = [B]190[/B]

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the en

Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the entire 175 page book?
Set up a proportion of pages to minutes where m is the number of minutes needed to read 175 pages:
7/5 = 175/m
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=175&den1=5&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine [/URL]and we get:
m = [B]125 minutes or 2 hours and 5 minutes[/B]