total - comprising the whole number or amount

1 apartment equals 10 window each window cost $79.30 there are 30 apartments what is the total for r

1 apartment equals 10 window each window cost $79.30 there are 30 apartments what is the total for replacing all the windows.
30 apartments * 10 windows per apartment * $79.30 per window = [B]$23,790[/B]

1 Die Roll

Free 1 Die Roll Calculator - Calculates the probability for the following events in the roll of one fair dice (1 dice roll calculator or 1 die roll calculator):

* Probability of any total from (1-6)

* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)

* The total being even

* The total being odd

* The total being a prime number

* The total being a non-prime number

* Rolling a list of numbers i.e. (2,5,6)

* Simulate (n) Monte Carlo die simulations.

1 die calculator

* Probability of any total from (1-6)

* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)

* The total being even

* The total being odd

* The total being a prime number

* The total being a non-prime number

* Rolling a list of numbers i.e. (2,5,6)

* Simulate (n) Monte Carlo die simulations.

1 die calculator

1 rabbit saw 6 elephants while going to the river. Every elephant saw 2 monkeys going towards the ri

1 rabbit saw 6 elephants while going to the river. Every elephant saw 2 monkeys going towards the river. Every monkey holds 1 parrot in their hands. How many animals are going towards the river?
[LIST]
[*]1 rabbit = 1
[*]6 elephants per rabbit = 6
[*]2 monkeys per elephant = 12
[*]1 parrot per monkey = 12 parrots
[*][B]31 total animals[/B]
[/LIST]

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls?

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls?
If 1/3 are boys, then the number of boys is:
600 * 1/3
600/3
We [URL='https://www.mathcelebrity.com/fraction.php?frac1=600%2F3&frac2=3%2F8&pl=Simplify']type this fraction into our search engine to simplify[/URL], and we get:
200
Now we need to find how many girls are at the school:
Girls = Total Students - Boys
Girls = 600 - 200
Girls = [B]400[/B]

1/9 of all sales were for cash. If cash sales were $59,000, what were the total sales?

1/9 of all sales were for cash. If cash sales were $59,000, what were the total sales?
Let sales be s. We're given:
s/9 = 59000
To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=s&num2=59000&den1=9&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
s = [B]531000[/B]

12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37

12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
12 multiplied by this number:
12x
The product of 12x is reduced by 9
12x - 9
The phrase [I]the total is equal to[/I] means an equation, so we set 12x - 9 equal to 37:
[B]12x - 9 = 37[/B]

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students who want pancakes to the total number of students?
12/14 is the initial ratio. However, we can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F14&frac2=3%2F8&pl=Simplify']So we type 12/14 into our search engine and choose simplify.[/URL] We get:
6/7

149 cars are waiting to take a ferry across the channel each ferry can only hold 18 cars how many tr

149 cars are waiting to take a ferry across the channel each ferry can only hold 18 cars how many trips will it take to get all the cars across
Number of trips = Total Cars / Cars Per ferry trip
Number of trips = 149/18
Number of trips = 8.28 trips
We round up to the next integer and we have [B]9 trips[/B]

15 cats, 10 have stripes, 7 have stripes and green eyes, how many cats have just green eyes

Let G be green eyes and S be Stripes, and SG be Stripes and Green Eyes.
[U]Set up an equation[/U]
Total Cats = Green Eyes + Stripes - Green Eyes and Stripes
15 = G + 10 - 7
15 = G + 3
[U]Subtract 3 from each side:[/U]
[B]G = 12[/B]

21 the total of 21 and

21 the total of 21 and?
Let the number we want be n. We have:
21 = 21 + n
n must be [B]0[/B], since 21 = 21

25 boxes are loaded on a truck. If each box weighs 22 kg, what is the total weight of the load

25 boxes are loaded on a truck. If each box weighs 22 kg, what is the total weight of the load?
Total Weight = Number of boxes * weight per box
Total Weight = 25 * 22 kg
Total Weight = [B]550 kg[/B]

250 students have iPhones. This is one third of the population. How many students are there in total

250 students have iPhones. This is one third of the population. How many students are there in total?
Let the population be p. We're given:
1/3p = 250
Cross multiply:
p = 250 * 3
p = [B]750[/B]

26 students 15 like vanilla 16 like chocolate. 3 do not like either flavour. How many like both vani

26 students 15 like vanilla 16 like chocolate. 3 do not like either flavour. How many like both vanilla and chocolate
Define our people:
[LIST=1]
[*]We have Vanilla Only
[*]Chocolate Only
[*]Both Vanilla and Chocolate
[*]Neither Vanilla Nor Chocolate
[*]Add up 1-4 to get our total
[/LIST]
Total = Vanilla Only + Chocolate Only - Vanilla and Chocolate + Neither
26 = 15 + 16 - V&C + 3
26 = 34 - V&C
Subtract 34 from each side
-V&C = -8
Multiply each side by -1
[B]V&C = 8[/B]

2755 students were surveyed: 896 chose a falcon, 937 chose a ram, and 842 chose a panther. The remai

2755 students were surveyed: 896 chose a falcon, 937 chose a ram, and 842 chose a panther. The remaining did not vote. What is the probability that the students choice was a panther?
P(Panther) = Panther Choices / Total Students
P(Panther) = 842/2,755
P(Panther) = [B]0.3056[/B]

28 students in class and 16 are boys what is percent of girls?

28 students in class and 16 are boys what is percent of girls?
Calculate the number of girls:
Girls = Total Students - Boys
Girls = 28 - 16
Girls = 12
The percent of girls is found by this formula:
Percent of Girls = 100 * Number of Girls / Number of Students
Percent of Girls = 100 * 12 / 28
Percent of Girls = 1,200 / 28
Percent of Girls = [B]42.86%[/B]

3 boys share 100 in the ratio 1:2:2. how much each boy will get?

3 boys share 100 in the ratio 1:2:2. how much each boy will get?
Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100
A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c
Therefore, our total group is 1 + 2 + 2 = 5
[SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE]
Expected Number of Item A = 1 x 100/5
Expected Number of Item A = 100/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item A = 20/1
Expected Number of Item A = [B]20[/B]
[SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE]
Expected Number of Item B = 2 x 100/5
Expected Number of Item B = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item B = 40/1
Expected Number of Item B = [B]40[/B]
[SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE]
Expected Number of Item C = 2 x 100/5
Expected Number of Item C = 200/5
Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5
Expected Number of Item C = 40/1
Expected Number of Item C = [B]40[/B]
[B]Final Answer:[/B]
(A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax
Figure out the total cost before the discount:
Total Cost before discount = Cases * Price per case
Total Cost before discount = 3 cases * $21.95 per case
Total Cost before discount = $65.85
Now, find the discounted value of the apples:
Discounted Apple Price = Total Cost before discount * (1 - discount percent)
Discounted ApplesPrice = $65.85 * (1 - 0.2) <-- 20% is the same as 0.2
Discounted ApplesPrice = $65.85 * 0.8
Discounted ApplesPrice = $52.68
Now, apply the sales tax to this discounted value to get the total bill:
Total Bill = Discounted Apple Price * (1 + tax rate)
Total Bill = $52.68 * (1 + .075) <-- 7.5% = 0.075
Total Bill = $52.68 * 1.075
Total Bill = [B]$56.63[/B]

3 friends went to dinner and their total bill was $19.50. They each brought $8. If a tip is typicall

3 friends went to dinner and their total bill was $19.50. They each brought $8. If a tip is typically between 15% and 20% of the bill do they have enough for dinner and tip?
15% tip:
19.50 * 1.15 = 22.43
20% tip:
19.50 * 1.2 = 23.4
3 friends each brought $8, so they have:
3 * 8 = $24
So the $24 [B]will cover both a 15% tip and a 20% tip[/B]

3 salads, 4 main dishes, and 2 desserts

3 salads, 4 main dishes, and 2 desserts
Total meal combinations are found by multiplying each salad, main dish, and dessert using the fundamental rule of counting.
The fundamental rule of counting states, if there are a ways of doing one thing, b ways of doing another thing, and c ways of doing another thing, than the total combinations of all the ways are found by a * b * c.
With 3 salads, 4 main dishes, and 2 desserts, our total meal combinations are:
3 * 4 * 2 = [B]24 different meal combinations.[/B]

3 tons of compost cost $3,600.00. What is the price per pound?

3 tons of compost cost $3,600.00. What is the price per pound?
1 ton = 2000 pounds, so 3 tons is:
3 * 2000 = 6000 pounds
Price per pound = Cost / Total pounds
Price per pound = 3600 / 6000
Price per pound = [B]$0.60 per pound[/B]

3.50 per pound. you bought 18.25 worth of strawberries

3.50 per pound. you bought 18.25 worth of strawberries
The question asks for unit cost.
Unit Cost = Total Cost / Total Quantity
Unit Cost = 18.25 / 3.50
Unit Cost = [B]5.21[/B]

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the program, how many workers are employed at this company?
We read this as 3/5 of the total workers employed at the company equals 24. Let w be the number of workers. We have the following equation:
3/5w = 24
Run [URL='http://www.mathcelebrity.com/1unk.php?num=3%2F5w%3D24&pl=Solve']3/5w = 24[/URL] through the search engine, we get [B]w = 40[/B].

32 girls and 52 boys were on an overseas learning trip . They were divided into as many groups as po

32 girls and 52 boys were on an overseas learning trip . They were divided into as many groups as possible where the number of groups of girls and the number of groups of boys is the same .how many boys and how many girls were in each group
We want a number such that our total members divided by this number equals our group size.
We take the greatest common factor (32,52) = 4
Therefore, we have:
[LIST]
[*][B]32/4 = 8 girls in each group[/B]
[*][B]52/4 = 13 boys in each group[/B]
[/LIST]

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many s

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?
Calculate the students in buses:
Students in buses = Total Students - Students in Cars
Students in buses = 331 - 7
Students in buses = 324
Calculate the students in each bus
Students in each bus = Students in buses / Number of Buses
Students in each bus = 324 / 6
Students in each bus = [B]54[/B]

3timesanumberdecreasedby3

A necklace chain costs $15. Beads cost $2.50 each. You spend a total of $30 on a necklace and beads before tax. How many beads did you buy in addition to the necklace?
Let the number of beads be b. We're given the following equation:
2.5b + 15 = 30
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5b%2B15%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]6[/B]

4 people like ketchup, 1 person likes tomato. How many people like ketchup or tomato?

4 people like ketchup, 1 person likes tomato. How many people like ketchup or tomato?
[I]Or[/I] means we add. We want to add people that like both ketchup and tomatoes.
4 ketchup + 1 tomato = [B]5[/B] total people

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The rema

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The remaining 30 passengers are girls. How many passengers are on the plane?
Add up the percents:
41% + 36% + 11% = 88%
This means that (100% - 88% = 12%) are girls.
So if the total amount of passengers on the plane is p, we write 12% s 0.12, and we have:
0.12p = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=0.12p%3D30&pl=Solve']Type this equation into our search engine[/URL], and we get:
p = [B]250[/B]

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost wa

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool
Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations:
[LIST=1]
[*]a + c = 414
[*]2a + 1.75c = 755.25
[/LIST]
We have a simultaneous equations. You can solve this any of 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
Whichever method you choose, you get the same answer:
[LIST]
[*][B]a = 123[/B]
[*][B]c = 291[/B]
[/LIST]

45 water balloons were given to 9 children. If each child received the same number of water balloons

45 water balloons were given to 9 children. If each child received the same number of water balloons, how many water balloons did each child receive?
Water Balloons per child = Total Water Balloons / Number of Children
Water Balloons per child = 45/9
Water Balloons per child = [B]5[/B]

4800$ salary spent 12% on clothes 20% on house rent how much money is she left with

4800$ salary spent 12% on clothes 20% on house rent how much money is she left with
12% on clothes plus 20% on house rent = 32% total spendings.
If she spent 32%, that means she's left with:
100% - 32% = 68%
So we want 68% of 4800.
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=68&den1=4800&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type [I]68% of 4800 [/I]into our search engine[/URL] and we get:
[B]3,264[/B]

5 children share 50 pencils. How many pencils does each child get

5 children share 50 pencils. How many pencils does each child get
Pencils per child = Total Pencils / Total children
Pencils per child = 50/5
Pencils per child = [B]10[/B]

5 times the total of 60 and x

5 times the total of 60 and x
The total of 60 and x means we add:
60 + x
5 times the total means we multiply the sum by 5
5(60 + x)

5/8 Of a class are boys. what fraction of the class are girls

5/8 Of a class are boys. what fraction of the class are girls?
The total class equals 1. Since 5/8 are boys, we subtract 5/8 from 1:
1 - 5/8
But we can write 1 as 8/8. So we have
8/8 - 5/8
[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F8&frac2=5%2F8&pl=Subtract']Type this fraction operation into our search engine[/URL] and we get:
[B]3/8[/B] are girls

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced t

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced that this would save them approximately $108 million annually. Based on this information, calculate the average annual pay of a single union member
Let the full salary of the union members be s. Since 17% is 0.17, We're given:
0.17s = 108000000
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.17s%3D108000000&pl=Solve']type it in our search engine[/URL] and we get:
s = 635,294,117.65
Calculate the average annual pay of a single union member:
Average Pay = Total Pay / Number of Union Members
Average Pay = 635,294,117.65 / 5000
Average Pay = [B]127,058.82[/B]

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there?
Assumptions:
[LIST]
[*]Let the number of adults be a
[*]Let the number of kids be k
[/LIST]
Given with assumptions:
[LIST=1]
[*]a + k = 508
[*]2a + 1.25k = 885.50 (since cost = price * quantity)
[/LIST]
Rearrange equation (1) by subtracting c from each side to isolate a:
[LIST=1]
[*]a = 508 - k
[*]2a + 1.25k = 885.50
[/LIST]
Substitute equation (1) into equation (2):
2(508 - k) + 1.25k = 885.50
Multiply through:
1016 - 2k + 1.25k = 885.50
1016 - 0.75k = 885.50
To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get:
k = [B]174[/B]
Now, to solve for a, we substitute k = 174 into equation 1 above:
a = 508 - 174
a = [B]334[/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 numbers have a mean of 4. What is the total of the 6 numbers?

6 numbers have a mean of 4. What is the total of the 6 numbers?
Mean = Sum of numbers / Count of numbers
Plug our Mean of 4 and our count of 6 into this equation:
4 = Sum/Total of Numbers / 6
Cross multiply:
Sum/Total of Numbers = 6 * 4
Sum/Total of Numbers = [B]24[/B]

6 red marbles 9 green marbles and 5 blue marbles two marbles are drawn without replacement what is t

6 red marbles 9 green marbles and 5 blue marbles two marbles are drawn without replacement what is the probability of choosing a green and then a blue marble
First draw:
there are 6 red + 9 green + 5 blue = 20 marbles
We draw 9 possible green out of 20 total marbles = 9/20
Second draw:
We don't replace, so we have 6 red + 8 green + 5 blue = 19 marbles
We draw 5 possible blue of out 19 total marbles = 5/19
Our total probability, since each event is independent, is:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F20&frac2=5%2F19&pl=Multiply']9/20 * 5/19[/URL] = [B]9/76[/B]

63 oranges is shared among 3 boys in the ratio of 2:3:4 how many oranges will the second boy receive

63 oranges is shared among 3 boys in the ratio of 2:3:4 how many oranges will the second boy receive?
Total sharing is 2 + 3 + 4 = 10.
[LIST]
[*]Boy 2 = 3/10 * 63 = [B]18.9 oranges[/B]
[/LIST]

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that i

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that it is not gray
[U]Find the total shirts:[/U]
Total shirts = Black Shirts + White Shirts + Gray Shirts
Total shirts = 7 + 5 + 10
Total shirts = 22
[U]Calculate the probability of choosing a gray shirt:[/U]
P(Gray) = Number of Gray shirts / Total Shirts
P(Gray) = 10/22
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F22&frac2=3%2F8&pl=Simplify']type in 10/22 into our search engine, choose simplify[/URL], and we get:
P(Gray) = [B]5/11[/B]

7 out of every 30 students ride their bikes to school. There are 720 students. How many ride their b

7 out of every 30 students ride their bikes to school. There are 720 students. How many ride their bikes
Set up a proportion of students who ride their bike to total students where r is the number of students who ride their bikes:
7/30 = r/720
To solve this proportion for r, we [URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=r&den1=30&den2=720&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our calculation engine and we get:[/URL]
r = [B]168[/B]

76 subtracted from p is equal to the total of g and 227

76 subtracted from p is equal to the total of g and 227
We've got two algebraic expressions. Take them in pieces:
Part 1:
76 subtracted from p
We subtract 76 from the variable p
p - 76
Part 2:
The total of g and 227
The total means a sum, so we add 227 to g
g + 227
Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other:
[B]p - 76 = g + 227[/B]

79 cents in 7 coins

3 quarters = 0.25 * 3 = 0.75
4 pennies = 0.01 * 4 = 0.04
Total Coin Value = 0.75 + 0.04 = 0.79
[B]3 quarters, 4 pennies[/B]

85 bags of nuts are to be divided among 18 friends. Each bag contains 15 nuts. How many nuts will ea

85 bags of nuts are to be divided among 18 friends. Each bag contains 15 nuts. How many nuts will each friend get?
[B][U]Calculate the total nuts:[/U][/B]
Total Nuts = Total Bags * Nuts Per Bag
Total Nuts = 85 * 15
Total Nuts = 1,275
[B][U]Figure out how many nuts each person gets:[/U][/B]
Nuts per person = Total Nuts / Friends
Nuts per person = 1,275 / 18
Nuts per person = [B]70.83[/B]

9 friends were paid $385 to clean up the local lake. How much does each friend receive

9 friends were paid $385 to clean up the local lake. How much does each friend receive
Each friend gets:
Total Payment / Number of friends
$385/9
[B]$42.78[/B]

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in si

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in size. what is the total area of the field
The area of each plot is 11*7 = 77
With 9 workers, the total area of the field is:
9 * 77 = [B]693 sq feet[/B]

963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs?

963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs?
Set up equation to represent the total animals on the farm
Total Animals = Cows + Pigs + Sheep
Now plug in what is given
963 = 406 + Pigs + 159
Simplify:
Pigs + 565 = 963
Subtract 565 from each side
[B]Pigs = 398[/B]

A $650 television costs $702 after sales tax is figured in. What is the sales tax percentage?

A $650 television costs $702 after sales tax is figured in. What is the sales tax percentage?
[U]Calculate Sales Tax Amount:[/U]
Sales Tax Amount = Total Bill - Original Cost
Sales Tax Amount = 702 - 650
Sales Tax Amount = 52
[U]Calculate Sales Tax Percentage:[/U]
Sales Tax Percentage = 100% * Sales Tax Amount / Original Cost
Sales Tax Percentage = 100% * 52 / 650
Sales Tax Percentage = 100% * 0.08
Sales Tax Percentage = [B]8%[/B]

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and short response questions are worth 8 points each. Write a system of linear equations that represents this situation
Assumptions:
[LIST]
[*]Let m be the number of multiple choice questions
[*]Let s be the number of short response questions
[/LIST]
Since total points = points per problem * number of problems, we're given 2 equations:
[LIST=1]
[*][B]m + s = 20[/B]
[*][B]3m + 8s = 100[/B]
[/LIST]
We can solve this system of equations 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[B]m = 12, s = 8[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each pri

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800?
Let x be the number of $24 tickets, and y be the number of $40 tickets. We have:
[LIST=1]
[*]24x + 40y = 188,800
[*]x + y = 6,000
[*]Rearrange (2) to solve for x: x = 6000 - y
[*]Plug in (3) to (1):
[/LIST]
24(6000 - y) + 40y = 188800
144,000 - 24y + 40y = 188,800
16y + 144,000 = 188,800
Subtract 144,000 from each side:
16y = 44,800
Divide each side by 16
y = 2,800 ($40 tickets)
Plug this into (2)
x + 2,800 = 6000
Subtract 2,800 from each side:
x = 3,200 ($24 tickets)

A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball

A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball has an even number?
Even numbers in the bag are {2,4,6,8,10,12,14,16,18}
So we have 9 total even numbers.
Therefore, the probability of drawing an even number is [B]9/19[/B]

A bag contains 2 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosi

A bag contains 2 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosing a blue marble, replacing it, drawing a green marble, replacing it, and then drawing a red marble?
Calculate total marbles in the bag:
Total marbles in the bag = Red Marbles + Blue Marbles + Green Marbles
Total marbles in the bag = 2 + 3 + 4
Total marbles in the bag = 9
[U]First choice, blue marble[/U]
P(blue) = Total Blue Marbles / Total Marbles in the bag
P(blue) = 3/9
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see:
P(blue) = 1/3
[U]Second choice, green marble with all the marbles back in the bag after replacement[/U]
P(green) = Total Green Marbles / Total Marbles in the bag
P(green) = 4/9
[U]Third choice, red marble with all the marbles back in the bag after replacement[/U]
P(red) = Total Red Marbles / Total Marbles in the bag
P(red) = 2/9
Since each event is independent, we multiply each probability:
P(blue, green, red) = P(blue) * P(green) * P(red)
P(blue, green, red) = 1/3 * 4/9 * 2/9
P(blue, green, red) = [B]8/243[/B]

A bag contains 3 black, 4 red, 3 yellow, and 2 green marbles. What is the probability of drawing a b

A bag contains 3 black, 4 red, 3 yellow, and 2 green marbles. What is the probability of drawing a black and then a red marble out of the bag without replacing the black marble before drawing the red marble?
The phrase [U][B]without replacement[/B][/U] is a huge clue on this problem.
Take each draw and calculate the probability.
Draw 1: P(Drawing a red)
P(Drawing a red) = Total Red marbles n the jar / Total marbles in the jar
P(Drawing a red) = 4/12
4/12 simplifies to 1/3 using a common factor of 4:
P(Drawing a red) = 1/3
Draw 2: P(Drawing a black)
P(Drawing a black) = Total Black marbles in the jar / Total marbles in the jar
[I]We drew one red marble already. Without replacement means we do not put it back. Therefore, we have 12 - 1 = 11 marbles left in the jar.[/I]
P(Drawing a black) = 3/11
The question asks, what is the the following probability:
P(Drawing a Red, Drawing a Black)
Because each draw is [I][U]independent[/U], [/I]we multiply each draw probability together:
P(Drawing a Red, Black) = P(Drawing a Red) * P(Drawing a Black)
P(Drawing a Red, Black) = 1/3 * 3/11
P(Drawing a Red, Black) = [B]1/11[/B]

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. another m

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same color.
[LIST]
[*]Total number of marbles in the bag is 3 + 4 = 7.
[*]The problem asks for the probability of (RR) [I]or[/I] (BB).
[*]It's worthy to note we are replacing the balls after each draw, which means we always have 7 to draw from
[/LIST]
Since each draw is independent, we take the product of each event for the total event probability.
P(RR) = 3/7 * 3/7 = 9/49
P(BB) = 4/7 * 4/7 = 16/49
We want to know P(RR) + P(BB)
P(RR) + P(BB) = 9/49 + 16/49 = 25/49
[MEDIA=youtube]26F9vjsgNGs[/MEDIA]

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random f

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random from the bag. What is P(blue)
P(blue) = Number of blue marbles / Total Marbles
P(blue) = 5 / (5 + 6 + 4)
P(blue) = 5/15
We can reduce this. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']type in 5/15 into our search engine, choose simplify[/URL], and we get:
P(blue) = [B]1/3[/B]

A bag contains 666 red balls, 444 green balls, and 333 blue balls. If we choose a ball, then another

A bag contains 666 red balls, 444 green balls, and 333 blue balls. If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be red?
[U]Calculate total number of balls to start:[/U]
Total Balls = Red Balls + Green Balls + Blue Balls
Total Balls = 666 + 444 + 333
Total Balls = 1,443
[U]Calculate the probability of drawing a green ball on the first pick:[/U]
P(Green) = Green Balls / Total Balls
P(Green) = 444/1443
P(Green) = 0.30769
[U]Calculate the probability of drawing a red ball on the second pick (without replacement):[/U]
Total Balls decrease by 1, since we do not replace. So Total Balls = 1,443 - 1 = 1,442
P(Red) = Red Balls / Total Balls
P(Red) = 666/1442
P(Red) = 0.46186
Now, we want the probability of Green, Red in that order.
Since each event is independent, we multiply the event probabilities
P(Green, Red) = P(Green) * P(Red)
P(Green, Red) = 0.30769 * 0.46186
P(Green, Red) = [B]0.14211[/B]

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be rando

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be randomly selected from the bag . What is the probability that the tile selected will be green
P(green) = Number of green tiles / Total Tiles
P(green) = 6 / (3 + 6 + 3)
P(green) = 6 / 12
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F12&frac2=3%2F8&pl=Simplify']type in 6/12 into our search engine, pick simplify[/URL], and we get:
P(green) = [B]1/2 or 0.5[/B]

A bag has 3 red, 5 blue, and 2 yellow pieces of candy. What is the theoretical probability of drawin

A bag has 3 red, 5 blue, and 2 yellow pieces of candy. What is the theoretical probability of drawing a blue piece of candy
P(Blue) = Blue Candies / Total Candies
P(Blue) = 5 / (3 + 5 + 2)
P(Blue) = 5 / 10
We can [URL='https://www.mathcelebrity.com/search.php?q=5%2F10&x=0&y=0']simplify this using our GCF calculator[/URL] and we get:
P(Blue) = [B]1/2[/B]

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purch

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 150 feet.
The area of a rectangle is length * width, so we have:
A = 290 * 150
A = 43,500 sq ft.
Now, to find the number of bags needed for a 300 square feet per bag of fertilizer, we have:
Bags Needed = Total Square Feet of Lawn / Square Feet covered per bag
Bags Needed = 43,500 / 300
Bags Needed = [B]145[/B]

A baker makes 387 cupcakes. They are sold in packs of six. How many full packs can be made? How many

A baker makes 387 cupcakes. They are sold in packs of six. How many full packs can be made? How many cupcakes are leftover?
Full packs = Lowest Rounded Integer of (Total cupcakes / packs)
Full packs = Lowest Rounded Integer of 387/6
Full Packs = Lowest Rounded Integer of 64.5
Full Packs = [B]64[/B]
Leftover = [URL='https://www.mathcelebrity.com/modulus.php?num=387mod6&pl=Calculate+Modulus']387 mod 6[/URL]
Leftover = [B]3[/B]

A baker needs 7 eggs to bake a cake . He has 150 eggs to bake a cake . How many cakes can he bake

A baker needs 7 eggs to bake a cake . He has 150 eggs to bake a cake . How many cakes can he bake
Total Cakes He can Bake = Total Eggs / Eggs Per Cake
Total Cakes He can Bake = 150/7
Total Cakes He can Bake = 21.42 or [B]21 full cakes[/B]

A bakery received a shipment of 4,554 peaches. If it takes 9 peaches to bake a peach pie, how many p

A bakery received a shipment of 4,554 peaches. If it takes 9 peaches to bake a peach pie, how many peach pies can the bakery make?
Total Pies = Total Peaches / 9
Total Pies = 4,554 / 9
Total Pies = [B]506[/B]

A bakery sells 349 pieces pande coco in a day. About how many pande coco bread can bakery shop sell

A bakery sells 349 pieces pande coco in a day. About how many pande coco bread can bakery shop sell in 25 days?
Total pieces of coco = Pieces per day * Number of Days
Total pieces of coco = 349 * 25
Total pieces of coco = [B]8,725[/B]

A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height fr

A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. The ball continues to bounce half the height of the previous bounce each time. How far will the ball have traveled when it hits the ground for the fifth time?
Take the top of the bounces one at a time:
[LIST=1]
[*]Ball is dropped 12 feet and it bounces up to 6 feet
[*]Ball drops 6 feet back down and bounces up to 3 feet up
[*]Ball drops 3 feet back down and bounces up to 1.5 feet up
[*]Ball drops 1.5 feet down and bounces up to 0.75 feet up
[*]Bounce 5 is 0.75 feet down
[/LIST]
[U]Total distance travelled:[/U]
12 + 6 + 6 + 3 + 3 + 1.5 + 1.5 + 0.75
[B]33.75 feet[/B]

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-f

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-fourths the height of the previous bounce. Find the total vertical distance travelled by the all in ten bounces.
The height of each number bounce (n) is shown as:
h(n) = 6(0.75)^n
We want to find h(10)
h(n) = 6(0.75)^n
Time Height
0 6
1 4.5
2 3.375
3 2.53125
4 1.8984375
5 1.423828125
6 1.067871094
7 0.8009033203
8 0.6006774902
9 0.4505081177
10 0.3378810883
Adding up each bounce from 1-10, we get:
16.98635674
Since vertical distance means both [B]up and down[/B], we multiply this number by 2 to get:
16.98635674 * 2 = 33.97271347
Then we add in the initial bounce of 6 to get:
33.97271347 + 6 = [B]39.97271347 feet[/B]

A barn contains cows, ducks, and a 3-legged dog named Tripod. There are twice as many cows as ducks

A barn contains cows, ducks, and a 3-legged dog named Tripod. There are twice as many cows as ducks in the barn and a total of 313 legs. How many ducks are there in the barn?
[LIST]
[*]Let the number of ducks be d. Duck legs = 2 * d = 2d
[*]Number of cows = 2d. Cow legs = 4 * 2d = 8d
[*]1 dog Tripod has 3 legs
[/LIST]
Total legs:
2d + 8d + 3 = 313
Solve for [I]d[/I] in the equation 2d + 8d + 3 = 313
[SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE]
(2 + 8)d = 10d
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
10d + 3 = + 313
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 3 and 313. To do that, we subtract 3 from both sides
10d + 3 - 3 = 313 - 3
[SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE]
10d = 310
[SIZE=5][B]Step 5: Divide each side of the equation by 10[/B][/SIZE]
10d/10 = 310/10
d = [B]31[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=2d%2B8d%2B3%3D313&pl=Solve']Source[/URL]

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many dif

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last.
(This means that 8 players are taken from the position players and one pitcher is then added at the end of the lineup.)
First 8 positions:
[URL='https://www.mathcelebrity.com/permutation.php?num=15&den=8&pl=Permutations']15P8[/URL] = 259,459,200
For the pitcher, we can have 10 different possibilities for the 9th player:
259,459,200 x 10 = [B]2,594,592,000 ways[/B]

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approxima

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approximately what percent of the games did the team win?
Using our percentage calculators, we type the following statements into our search engine and get:
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=45&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']45% of 30[/URL] = 13.5
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=65&den1=60&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']65% of 60[/URL] = 39
For a total of 52.5 games won
The team played 30 + 60 = 90 games. So we want to know the pecent:
[URL='https://www.mathcelebrity.com/perc.php?num=52&den=90&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']52/90[/URL] = [B]57.78%[/B]

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is the total price of the bedroom set if it is bought while on sale?
[U]Calculate the sale price:[/U]
Sale Price = Normal Price * (1 - Sales Percentage)
[U]With our sales percentage of 15% = 0.15, we have:[/U]
Sale Price = 1100 * (1 - 0.15)
Sale Price = 1100 * (0.85)
Sale Price = 935
[U]Calculate post tax amount:[/U]
Post tax amount = Sale Price * (1 + Tax Percentage)
[U]With our tax percentage of 2% = 0.02, we have:[/U]
Post tax amount = 935 * (1 + 0.02)
Post tax amount = 935 * (1.02)
Post tax amount = [B]$953.70[/B]

A bill at a resturant came to $95.75. There is 7.5% sales tax added on. You want to leave a 20% tip

A bill at a resturant came to $95.75. There is 7.5% sales tax added on. You want to leave a 20% tip to the total bill, after tax. How much money will you need to leave for the bill altogether?
Since the tip is [I]after tax[/I], we have:
Total Bill = Pre-tax Bill * (1 + Sales Tax Percent) * (1 + Tip Percent)
Total Bill = $95.75 * (1 + 0.07) * (1 + 0.2)
Total Bill = $95.75 * 1.07 * 1.2
Total Bill = [B]$122.94[/B]

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat t

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat today. All the rides are full except for the first ride. How many rides are given?
582 passengers on the boat
Let r be the number of rides
So we want to find r when:
582r = 13105
To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=582r%3D13105&pl=Solve']type this equation into our math engine[/URL] and we get:
r = 22.517
If we round this down, setting 0.517 rides as the first ride, we get:
r = [B]22
[MEDIA=youtube]0J2YRPzKsoU[/MEDIA][/B]

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To th

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To the nearest hundredth of a kilometer per hour, how fast was it going?
Distance = Rate * Time
We're given t = 32, and d = 597. Using our [URL='https://www.mathcelebrity.com/drt.php?d=+597&r=+&t=32&pl=Calculate+the+missing+Item+from+D%3DRT']distance, rate, and time calculator[/URL], we get:
r = [B]18.656 km/hr[/B]

A book cost $8.50 without tax. If the tax rate is 7%, what is the total cost of the book including t

A book cost $8.50 without tax. If the tax rate is 7%, what is the total cost of the book including tax?
8.50 * 1.07 = [B]$9.10[/B]

A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the

A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the other, without replacement. please show the steps.
(a) The first two apples are green. What is the probability that the third apple is red?
(b) What is the probability that exactly two of the three apples are red?
a) You have 22 red apples left and 1 green left leaving 23 total apples left. Therefore, probability of red is
[B]P(R) = 22/23[/B]
b) Determine our sample space to select exactly two red apples in three picks.
[LIST=1]
[*]RRG
[*]RGR
[*]GRR
[/LIST]
[U]Now determine the probabilities of each event in the sample space[/U]
P(RRG) = 22/25 * 21/24 * 3/23 = 0.1004
P(RGR) = 22/25 * 3/24 * 21/23 = 0.1004
P(GRR) = 3/25 * 22/24 * 21/23 = 0.1004
[U]We want the sum of the three probabilities[/U]
P(RRG) + P(RGR) + P(GRR) = 0.1004 + 0.1004 + 0.1004
P(RRG) + P(RGR) + P(GRR) = 3(0.1004)
P(RRG) + P(RGR) + P(GRR) = [B]0.3012[/B]

A box contains 4 red jellies, 6 blue jellies and 5 yellow jellies. What is the probability that a j

A box contains 4 red jellies, 6 blue jellies and 5 yellow jellies. What is the probability that a jelly chosen randomly from the box is not red?
Calculate Total Jellies:
Total Jellies = Red Jellies + Blue Jellies + Yellow Jellies
Total Jellies = 4 + 6 + 5
Total Jellies = 15
Not choosing a red jelly means choosing a blue [B]or[/B] yellow jelly
P(not red jelly) = P(blue) + P(Yellow)
P(not red jelly) = (Blue Jelly + Yellow Jelly) / Total Jellies
P(not red jelly) = (6 + 5)/15
P(not red jelly) = [B]11/15[/B]

A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probabilit

A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probability of drawing 2 black balls.
First draw probability of black is:
Total Balls in box = Black balls + white balls
Total Balls in Box = 5 + 2
Total Balls in Box = 7
P(Black) = Black Balls / Total balls in box
P(Black) = 5/7
Second draw probability of black (with no replacement) is:
Total Balls in box = Black balls + white balls
Total Balls in Box = 4 + 2
Total Balls in Box = 6
P(Black) = Black Balls / Total balls in box
P(Black) = 4/6
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we see that 4/6 is:
2/3
Since each event is independent, we can multiply them to find the probability of drawing 2 black balls:
P(Black, Black) = 5/7 * 2/3
[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F7&frac2=2%2F3&pl=Multiply']P(Black, Black)[/URL] = 10/21

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons . One

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected
[U]Calculate the probability of a plain pencil in the first box:[/U]
P(plain pencil in the first box) = Total Pencils / Total Objects
P(plain pencil in the first box) = 5 pencils / (5 pencils + 3 pens)
P(plain pencil in the first box) = 5/8
[U]Calculate the probability of a color pencil in the first box:[/U]
P(color in the second box) = Total Pencils / Total Objects
P(color in the second box) = 2 pencils / (2 pencils + 2 crayons)
P(color in the second box) = 2/4
We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Type 2/4 into our search engine[/URL] and we get 1/2
Now the problem asks for the probability that a plain pencil from the first box and a color pencil from the second box are selected.
Since each event is independent, we multiply them together to get our answer:
P(plain pencil in the first box, color in the second box) = P(plain pencil in the first box) * P(color in the second box)
P(plain pencil in the first box, color in the second box) = 5/8 * 1/2
P(plain pencil in the first box, color in the second box) = [B]5/16[/B]

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, i

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, it is not replaced, then another is chosen. What is the probability of choosing a red followed by a green?
We have 6 + 3 + 5 + 7 = 21 total pencils
P(Red on the first draw) = Total Red / Total pencils
P(Red on the first draw) = 3/21
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F21&frac2=3%2F8&pl=Simplify']P(Red on the first draw)[/URL] = 1/7
We're drawing without replacement, this means on the next draw, we have 21 - 1 = 20 pencils
P(Green on the second draw) = Total Green / Total pencils
P(Green on the second draw) = 5/20
[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']P(Green on the second draw) [/URL]= 1/4
Since each event is independent, we have:
P(Red on first, green on second) = P(Red on First) * P(green on second)
P(Red on first, green on second) = 1/7 * 1/4
P(Red on first, green on second) = [B]1/28[/B]

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils.

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils.
Removed means we subtract from the total. So Our equation is:
x - 6 = 54
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-6%3D54&pl=Solve']type it in our search engine [/URL]and we get:
x = [B]60[/B]

A box is filled with 10 green cards, 4 blue cards, and 4 brown cards. A card is chosen at random fr

A box is filled with 10 green cards, 4 blue cards, and 4 brown cards. A card is chosen at random from the box. What is the probability that it is a green or a brown card?
Calculate Total Cards:
10 green cards + 4 blue cards + 4 brown cards = 18 cards
"Or", means either or, so we want P(Green) + P(Brown)
[U]Find P(Green)[/U]
P(Green) = Green Cards / Total Cards
P(Green) = 10/18 <-- Simplify by dividing top and bottom by 2
P(Green)= 5/9 <-- Simplify by dividing top and bottom by 2
Find P(Brown)
P(Brown) = Brown Cards / Total Cards
P(Brown) = 4/18 <-- Simplify by dividing top and bottom by 2
P(Brown)= 2/9 <-- Simplify by dividing top and bottom by 2
P(Green) + P(Brown) = 5/9 + 2/9
P(Green) + P(Brown) = [B]7/9[/B]

A box of pencils weights 3.25 grams. If the teacher orders 14 boxes, how much would the pencils weig

A box of pencils weights 3.25 grams. If the teacher orders 14 boxes, how much would the pencils weigh?
Total Weight = Number of Boxes * Weight per box
Total Weight = 14 * 3.25
Total Weight = [B]45.5 grams[/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 bus holds 45 students. How many buses were taken on a field trip if 13 students travels by car and

A bus holds 45 students. How many buses were taken on a field trip if 13 students travels by car and total of 320 students went on a trip?
[U]Find the number of students who went on the bus:[/U]
Number of students who went on the bus = Total students on field trip - students who traveled by car
Number of students who went on the bus = 320 - 13
Number of students who went on the bus = 307
Calculate the number of buses needed:
Number of buses needed = Number of students who went on the bus / Bus Capacity
Number of buses needed = 307 / 45
Number of buses needed = 6.822
We round up for a full bus to get [B]7 buses[/B]

A cable company charges $75 for installation plus $20 per month. Another cable company offers free i

A cable company charges $75 for installation plus $20 per month. Another cable company offers free installation but charges $35 per month. For how many months of cable service would the total cost from either company be the same
[U]Set ups the cost function for the first cable company C(m) where m is the number of months:[/U]
C(m) = cost per month * m + installation fee
C(m) = 20m + 75
[U]Set ups the cost function for the second cable company C(m) where m is the number of months:[/U]
C(m) = cost per month * m + installation fee
C(m) = 35m
The problem asks for m when both C(m) functions are equal. So we set both C(m) functions equal and solve for m:
20m + 75 = 35m
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B75%3D35m&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]5[/B]

A cantaloupe weighs 3.8 pounds. About how much do 5 cantaloupes weigh?

A cantaloupe weighs 3.8 pounds. About how much do 5 cantaloupes weigh?
Total Weight = Weight per cantaloupe * Total cantaloupes
Total Weight = 3.8 * 5
Total Weight = [B]19 pounds[/B]

A car cost 500 how much does 5 cars cost

A car cost 500 how much does 5 cars cost
Total cost = Number of cars * cost per cars
Total cost = 5 * 500
Total cost = [B]2500[/B]

A car repair bill was $441. This included $153 for parts and four hours of labor . Find the hourly r

A car repair bill was $441. This included $153 for parts and four hours of labor . Find the hourly rate I was charge for labor
Subtract the cost of parts from the total repair bill to get the labor cost:
Labor Cost = Total Bill - Parts Cost
Labor Cost = 441 - 153
Labor Cost = 288
Labor Cost can be broken down into Labor divided by hours
Hourly Labor Rate = Labor Cost / Labor Hours
Hourly Labor Rate = = 288 / 4
Hourly Labor Rate = [B]72[/B]

A card is drawn from a pack of 52 cards. The probability that the card drawn is a red card is

A card is drawn from a pack of 52 cards. The probability that the card drawn is a red card is
The deck is split evenly between red and black cards.
So we have 52/2 = 26 red cards
P(Red) = # of Red Cards / Total Deck Cards
P(Red) = 26/52
We can simplify this fraction. [URL='https://www.mathcelebrity.com/fraction.php?frac1=26%2F52&frac2=3%2F8&pl=Simplify']Using our fraction calculator[/URL], we get:
P(Red) = [B]1/2 or 0.5[/B]

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25¢ per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned?
Calculate the cost of the staircase cleaning.
Staircase cost = $1.30 * steps
Staircase cost = $1.30 * 14
Staircase cost = $18.20
Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet.
Carpet cost = $253.95 - $18.20
Carpet cost = $235.75
Now, the remaining carpet cost can be written as:
75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned
Multiply through and simplify:
75 + 0.25s - 45 = $235.75
Combine like terms:
0.25s + 30 = 235.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B30%3D235.75&pl=Solve']Type this equation into our search engine[/URL] to solve for s, and we get:
s = [B]823[/B]

A case of meatball costs $19.09. There are 320 meatballs in a case. How much does 1 meatball cost?

A case of meatball costs $19.09. There are 320 meatballs in a case. How much does 1 meatball cost?
Cost per meatball = Cost of case / Total Meatballs per case
Cost per meatball = $19.09 / 320
Cost per meatball = [B]$0.06 per meatball[/B]

A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills t

A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills total, then how many of each does the register contain?
Let f be the number of $5 dollar bills and t be the number of $20 bills. We're given the following equations:
[LIST=1]
[*]f + t = 15
[*]5f + 20t = 180
[/LIST]
We can solve this system of equations 3 ways. We get [B]t = 7[/B] and [B]f = 8[/B].
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have?
Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations:
[LIST=1]
[*]a + b = 44
[*]10a + 20b = 730
[/LIST]
We rearrange equation 1 in terms of a. We subtract b from each side and we get:
[LIST=1]
[*]a = 44 - b
[*]10a + 20b = 730
[/LIST]
Now we substitute equation (1) for a into equation (2):
10(44 - b) + 20b = 730
Multiply through to remove the parentheses:
440 - 10b + 20b = 730
Group like terms:
440 + 10b = 730
Now, to solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=440%2B10b%3D730&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]29
[/B]
To get a, we take b = 29 and substitute it into equation (1) above:
a = 44 - 29
a = [B]15
[/B]
So we have [B]15 ten-dollar bills[/B] and [B]29 twenty-dollar bills[/B]

A cashier has a total of 52 bills in her cash drawer. There are only $10 bills and $5 bills in her

A cashier has a total of 52 bills in her cash drawer. There are only $10 bills and $5 bills in her drawer. The value of the bills is $320. How many $10 bills are in the drawer?
Let f be the amount of $5 bills in her drawer. Let t be the amount of $10 bills in her drawer. We're given two equations:
[LIST=1]
[*]f + t = 52
[*]5f + 10t = 320
[/LIST]
We have a system of equations. We can solve this 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we choose, we get:
f = 40 and t = 12
So the answer for how many $10 bills are in the drawer is [B]12[/B].
Let's check our work for equation 1:
40 + 12 ? 52
52 = 52 <-- Confirmed
Let's check our work for equation 2:
5(40) + 10(12) ? 320
200 + 120 ? 320
320 = 320 <-- Confirmed

A catering service offers 4 appetizers, 12 main courses, and 9 desserts. A customer is to select 3 a

A catering service offers 4 appetizers, 12 main courses, and 9 desserts. A customer is to select 3 appetizers, 10 main courses, and 5 desserts for a banquet. In how many ways can this be done?
We use combinations, so we have:
[LIST]
[*][URL='https://www.mathcelebrity.com/permutation.php?num=4&den=3&pl=Combinations']4C3 appetizers[/URL] = 4
[*][URL='https://www.mathcelebrity.com/permutation.php?num=12&den=10&pl=Combinations']12C10 main courses[/URL] = 66
[*][URL='https://www.mathcelebrity.com/permutation.php?num=9&den=5&pl=Combinations']9C5 desserts[/URL] = 126
[/LIST]
We multiply each of these together to get our total combinations:
4 * 66 * 126 = [B]33,264[/B]

A cell phone company charges 8$ per minute. How much do you pay for 60 minutes?

A cell phone company charges 8$ per minute. How much do you pay for 60 minutes?
Calculate the total bill:
Total Bill = Cost per minute * number of minutes
Total Bill = $8 * 60
Total Bill = [B]$480[/B]

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 ce

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 cents. If you use your cell phone for at least 200 minutes a month, write a function C(x) that represents the total cost per x minutes.
We add the flat rate per month to 5% of the number of minutes [U]over[/U] 200:
[B]C(x) = 20 + 0.05(x - 200)[/B]

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute c

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute costs $.35. This month you used 750 minutes. How much do you owe
[U]Find the overage minutes:[/U]
Overage Minutes = Total Minutes - Free Minutes
Overage Minutes = 750 - 600
Overage Minutes = 150
[U]Calculate overage cost:[/U]
Overage Cost = Overage Minutes * Overage cost per minute
Overage Cost = 150 * 0.35
Overage Cost = $52.5
Calculate total cost (how much do you owe):
Total Cost = Monthly Fee + Overage Cost
Total Cost = $49.99 + $52.50
Total Cost = [B]$102.49[/B]

A chicken farm produces ideally 700,000 eggs per day. But this total can vary by as many as 60,000 e

A chicken farm produces ideally 700,000 eggs per day. But this total can vary by as many as 60,000 eggs. What is the maximum and minimum expected production at the farm?
[U]Calculate the maximum expected production:[/U]
Maximum expected production = Average + variance
Maximum expected production = 700,000 + 60,000
Maximum expected production = [B]760,000[/B]
[U]Calculate the minimum expected production:[/U]
Minimum expected production = Average - variance
Minimum expected production = 700,000 - 60,000
Minimum expected production = [B]640,000[/B]

A city doubles its size every 48 years. If the population is currently 400,000, what will the popula

A city doubles its size every 48 years. If the population is currently 400,000, what will the population be in 144 years?
Calculate the doubling time periods:
Doubling Time Periods = Total Time / Doubling Time
Doubling Time Periods = 144/48
Doubling Time Periods = 3
Calculate the city population where t is the doubling time periods:
City Population = Initital Population * 2^t
Plugging in our numbers, we get:
City Population = 400,000 * 2^3
City Population = 400,000 * 8
City Population = [B]3,200,000[/B]

A class is made up of 6 boys and 12 girls. Half of the girls wear glasses. A student is selected at

A class is made up of 6 boys and 12 girls. Half of the girls wear glasses. A student is selected at random from the class. What is the probability that the student is a girl with glasses?
1/2 of 6 is 3. So we want the probability we pick any of the 3 girls wearing glasses.
We have a total of 6 + 12 = 18 people.
Our probability is [B]3/18, or 1/6[/B].

A class of n students was raising money for a field trip. They have earned $800 so far. Each student

A class of [I]n[/I] students was raising money for a field trip. They have earned $800 so far. Each student plans to work [I]x[/I] more hours at a wage of [I]y[/I] dollars per hour. When they are done, how much money will they have earned?
Class of n students * x more hours worked * y dollars per hour = xyn
Total dollars earned includes the $800 already earned:
$800 + xyn

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. En

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. Enter an equation that represents the total number of guppies, y, in the fish tank.
The phrase [I]4 times as many[/I] means we multiply the goldfish (x) by 4 to get the number of guppies (y):
[B]y = 4x[/B]

a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 3

a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 30 pencils?
Set up a function, P(w), where w is the number of weeks, and P(w) is the total amount of pencils after w weeks. We have:
P(w) = 3w + 7
We want to know what w is when P(w) = 30
3w + 7 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B7%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
w = 7.6667
We round up to the nearest integer, so we get [B]w = 8[/B]

A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3

A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3 times as many nickels as dimes.
Let n be the number of nickels. Let d be the number of dimes. We're give two equations:
[LIST=1]
[*]n = 3d
[*]0.1d + 0.05n = 8.50
[/LIST]
Plug equation (1) into equation (2) for n:
0.1d + 0.05(3d) = 8.50
Multiply through:
0.1d + 0.15d = 8.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.1d%2B0.15d%3D8.50&pl=Solve']Type this equation into our search engine[/URL] and we get:
[B]d = 34[/B]
Now, we take d = 34, and plug it back into equation (1) to solve for n:
n = 3(34)
[B]n = 102[/B]

A college student earned $6000 during summer vacation working as a waiter in a popular restaurant. T

A college student earned $6000 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 8% and the rest at 6%. If the student received a total of $418 in interest at the end of the year, how much was invested at 8%?
[URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=6000&i1=8&i2=6&itot=418&pl=Calculate']Using our split fund interest calculator[/URL], we get:
[B]$2,900 invested at 8%[/B]
$3,100 invested at 6%

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes from now?
Calculate the doubling time periods:
Doubling Time Periods = Total Minutes From Now / Doubling Period in Minutes
Doubling Time Periods = 618/206
Doubling Time Periods = 3
Calculate the new population using the doubling time formula below where t is the number of doubling periods:
Population = Initial Population * 2^2
Population = 995 * 2^3
Population = 995 * 8
Population = [B]7,960[/B]

A combined total of $34,000 is invested in two bonds that pay 4% and 8.5% simple interest. The annua

A combined total of $34,000 is invested in two bonds that pay 4% and 8.5% simple interest. The annual interest is $2,350. How much is invested in each bond
Using our split fund interest calculator, we get;
[LIST]
[*][B]12,000[/B] in Fund 1
[*][B]22,000[/B] in Fund 2
[/LIST]

A combined total of $40,000 is invested in two bonds that pay 6% and 9% simple interest. The annual

A combined total of $40,000 is invested in two bonds that pay 6% and 9% simple interest. The annual interest is $3,210.00. How much is invested in each bond?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=40000&i1=6&i2=9&itot=3210&pl=Calculate']split fund interest calculator[/URL], we get:
Fund 1 at 6% = [B]13,000[/B]
Fund 2 at 9% =[B] 27,000[/B]

A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position

A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 12 faculty members and 15 students eligible to serve on the committee. In how many ways can the committee be formed?
We'll use combinations, so we have:
[LIST]
[*][URL='https://www.mathcelebrity.com/permutation.php?num=12&den=4&pl=Combinations']12 faculty members choose 4 faculty members --> 12 C 4[/URL] = 495
[*][URL='https://www.mathcelebrity.com/permutation.php?num=15&den=5&pl=Combinations']15 students choose 5 students --> 15 C 5[/URL] = 3,003
[/LIST]
To get the total committees, we multiply the total faculty member choices by the total student choices:
Total committees = total faculty members * total students
Total committees = 495 * 3,003
Total committees = [B]1,486,485[/B]

A committee of 6 students are being selected from a class of 10 girls and 8 boys. How many committee

A committee of 6 students are being selected from a class of 10 girls and 8 boys. How many committees are possible if three must be girls and 3 must be boys?
We want combinations. How many ways can we choose 3 boys from 8 boys:
[URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']8 choose 3[/URL] = 56
We want combinations. How many ways can we choose 3 girls from 10 girls:
[URL='https://www.mathcelebrity.com/permutation.php?num=10&den=3&pl=Combinations']10 choose 3[/URL] = 120
Our total choices are found by multiplying each event:
Total committees = (8 boys choose 3) * (10 girls choose 3)
Total committees = 56 * 120
Total committees = [B]6,720[/B]

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number of T-shirts for the school store. The total cost of the order was $1,520. Which equation can be used to find the number one f shirts ordered?
Set up the cost equation C(f) where f is the number of shirts:
C(f) = Cost per shirt * f + Shipping
We're given C(f) = 1520, Shipping = 22, and cost per shirt is 7, so we have:
[B]7f + 22 = 1520
[/B]
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=7f%2B22%3D1520&pl=Solve']type this equation in our search engine[/URL] and we get:
f = [B]214[/B]

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 100x dollars, w

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 + 100x dollars, where x is the number of units produced and sold. How many units will give a profit
Profit P(x) is given by:
R(x) - C(x)
So we have:
P(x) = 500x - (100x + 48,000)
P(x) = 500x - 100x - 48,000
P(x) = 400x - 48,000
A profit is found when P(x) > 0, so we have:
400x - 48000 > 0
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=400x-48000%3E0&pl=Solve']we type it into our search engine [/URL]and we get:
[B]x > 120[/B]

A company makes a puzzle that is made of 53 small plastic cubes. The puzzles are shipped in boxes th

A company makes a puzzle that is made of 53 small plastic cubes. The puzzles are shipped in boxes that each contain 52 puzzles. That boxes are loaded into trucks that each contain 53 boxes. What is the total number of small plastic cubes in each truck?
1 truck has 53 boxes, and each box contains 52 puzzles, and each puzzle has 53 small plastic cubes.
We have 53 * 52 * 53 = [B]146,068 plastic cubes[/B]

A company now has 4900 employees nationwide. It wishes to reduce the number of employees by 300 per

A company now has 4900 employees nationwide. It wishes to reduce the number of employees by 300 per year through retirements, until its total employment is 2560. How long will this take?
Figure out how many reductions are needed
4900 - 2560 = 2340
We want 300 per year for retirements, so let x equal how many years we need to get 2340 reductions.
300x = 2340
Divide each side by 300
x = 7.8 years.
If we want full years, we would do 8 full years

A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Eac

A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 350 nails. How many nails are there in 6 small boxes and 3 large boxes? How many nails are there in a small boxes and l large boxes?
[U]Calculate Small Nails[/U]
Small Nails = Small Nail Boxes * Nails per Box
Small Nails = 6 * 100
Small Nails = 600
[U]
Calculate Large Nails[/U]
Large Nails = Large Nail Boxes * Nails per Box
LargeNails = 3 * 350
Large Nails = 1,050
[U]Calculate Total Nails[/U]
Total Nails = Small Nails + Large Nails
Total Nails = 600 + 1,050
Total Nails = [B]1,650[/B]

a cookie jar contains 3 vanilla, 2 chocolate chip, and 7 gingersnap cookies. Of one cookie is taken

a cookie jar contains 3 vanilla, 2 chocolate chip, and 7 gingersnap cookies. Of one cookie is taken at random from the jar, what is the probability that it will be a vanilla cookie?
Total cookies = 3 + 2 + 7
Total cookies = 12
P(Vanilla) = Vanilla Cookies / Total Cookies
P(Vanilla) = 3/12
Simplified dividing top and bottom by 3, we have:
P(Vanilla) = [B]1/4[/B]

A cookie jar contains 8 cookies. There are 4 children. How many cookies will each child receive?

A cookie jar contains 8 cookies. There are 4 children. How many cookies will each child receive?
Cookies Per child = Total Cookies / Total Children
Cookies Per child = 8/4
Cookies Per child = [B]2[/B]

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8 1/4 cups, how much flour and how much sugar would it be?
Let f be the number of cups of sugar. And let f be the number of cups of flour. We're given two equations:
[LIST=1]
[*]f = 10s
[*]s + f = 8 & 1/4
[/LIST]
Substitute (1) into (2):
s + 10s = 8 & 1/4
11fs= 33/4 <-- 8 & 1/4 = 33/4
Cross multiply:
44s = 33
Divide each side by 44:
s= 33/44
Divide top and bottom by 11 and we get s [B]= 3/4 or 0.75[/B]
Now substitute this into (1):
f = 10(33/44)
[B]f = 330/44 or 7 & 22/44 or 7.5[/B]

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The tot

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The total value of the items is $825. How many coins are there?
Let c be the number of coins, and s be the number of stamps. We're given:
[LIST=1]
[*]c + s = 300
[*]3c + 1.5s = 825
[/LIST]
We have a set of simultaneous equations, or a system of equations. We can solve this 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]
No matter which way we pick, we get:
s = 50
c = [B]250[/B]

A cube is 1 meter long.What is the total length of all its edges?

A cube is 1 meter long.What is the total length of all its edges?
A cube has 12 edges.
12 edges x 1 meter for each edge = [B]12 meters[/B]

A cup of coffee cost $4 and a cup of tea cost $3.50. If ray has $40 and has bought 6 cups of coffee,

A cup of coffee cost $4 and a cup of tea cost $3.50. If ray has $40 and has bought 6 cups of coffee, find the maximum cups of tea he can buy
[U]Calculate total coffee spend:[/U]
Total coffee spend = Cost per Cup of Coffee * Cups of Coffee
Total coffee spend = 4 * 6
Total coffee spend = 24
[U]Calculate remaining amount to be spent on tea:[/U]
Remaining tea money = Starting Money - Total Coffee spend
Remaining tea money = 40 - 24
Remaining tea money = 16
[U]Calculate cups of tea Ray can buy:[/U]
Cups of tea Ray can buy = Remaining Tea money / Cost per cup of tea
Cups of tea Ray can buy = 16/3.50
Cups of tea Ray can buy = 4.57142857143
Since Ray can't buy partial cups, we round down and we get:
Cups of tea Ray can buy = [B]4[/B]

A customer buys 5 pounds of apples at $0.79 a pound. They hand the cashier a $10 bill. How much chan

A customer buys 5 pounds of apples at $0.79 a pound. They hand the cashier a $10 bill. How much change will they get back?
Calculate the total bill:
Total Bill = Pounds of Apples * Cost per pound
Total Bill = 5 * 0.79
Total Bill = $3.95
Calculate Change:
Change = Money Offered - Total Bill
Change = $10 - $3.95
Change = [B]$6.05[/B]

A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with eithe

A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Let d be the number of days the skier attends.
Calculate the daily cost:
Daily Total Cost = Daily Cost + Rental Cost
Daily Total Cost = 62d + 30d
Daily Total Cost = 92d
Calculate Season Cost:
Season Total Cost = Season Fee + Rental Cost
Season Total Cost = 450 + 30d
Set the daily total cost and season cost equal to each other:
450 + 30d = 92d
[URL='https://www.mathcelebrity.com/1unk.php?num=450%2B30d%3D92d&pl=Solve']Typing this equation into the search engine[/URL], we get d = 7.258.
We round up to the next full day of [B]8[/B].
Now check our work:
Daily Total Cost for 8 days = 92(8) = 736
Season Cost for 8 days = 30(8) + 450 = 240 + 450 = 710.
Therefore, the skier needs to go at least [B]8 days[/B] to make the season cost less than the daily cot.

A deck of cards costs f dollars. If Sharon bought 9 decks of cards, how much did she spend?

A deck of cards costs f dollars. If Sharon bought 9 decks of cards, how much did she spend?
Calculate Total Cost:
Total Cost = Decks of Cards * Price per deck
Total Cost = [B]9f[/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 desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you dra

A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you draw out a pencil and then draw out a second pencil without returning the first pencil. What is the probability that the first pencil and the second pencil are both green?
We are drawing without replacement. Take each draw probability:
[LIST=1]
[*]First draw, we have a total of 10 + 7 + 8 = 25 pencils to choose from. P(Green) = 8/25
[*]Next draw, we only have 24 total pencils, and 7 green pencils since we do not replace. Therefore, we have P(Green)= 7/24
[/LIST]
Since both events are independent, we have:
P(Green) * P(Green) = 8/25 * 7/24
P(Green) * P(Green) = 56/600
Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=56&num2=600&num3=&pl=GCF']GCF Calculator[/URL], we see the greatest common factor of 56 and 600 is 8. So we divide top and bottom of the fraction by 8.
[B]P(Green) * P(Green) = 7/75[/B]

A dish company needs to ship an order of 893 glass bowls. If each shipping box can hold 19 bowls, ho

A dish company needs to ship an order of 893 glass bowls. If each shipping box can hold 19 bowls, how many boxes will the company need?
Number of boxes needed = Total bowls / Glass bowls per box
Number of boxes needed = 893/19
Number of boxes needed = [B]47[/B]

A drawer is filled with 9 black shirts , 6 white shirts, and 5 gray shirts one shirt is chosen at ra

A drawer is filled with 9 black shirts , 6 white shirts, and 5 gray shirts one shirt is chosen at random from the drawer find the probability that it is not a white shirt
P(Not White) = P(Black or Gray)
P(Black or Gray) = (Total Black + Total Gray)/Total Shirts
P(Black or Gray) = (9 + 5)/(9 + 6 + 5)
P(Black or Gray) = 14/20
Simplifying this [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F20&frac2=3%2F8&pl=Simplify']using our fraction simplify calculator[/URL], we get:
P(Black or Gray) = [B]7/10, or 0.7 or 70%[/B]

A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with

A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The Web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy?
Let t be the number of tickets. We have the following equation with ticket price, insurance, and flat fee:
167t + 19t + 16 = 1132
Combine like terms:
186t + 16 = 1132
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=186t%2B16%3D1132&pl=Solve']equation calculator[/URL], we have:
[B]t = 6[/B]

A family of 4 spent $78 at the exhibition. They spent $22 on rides and the rest on entrance fees. Ho

A family of 4 spent $78 at the exhibition. They spent $22 on rides and the rest on entrance fees. How much was the entrance fee per person
We need to find the entrance fee per person. So subtract the cost of rides from the total spend:
Entrance Fees = Total Spend - Cost of Rides
Entrance Fees = 78 - 22
Entrance Fees = 56
[U]Now find the entrance fee per person:[/U]
Entrance Fee Per Person = Entrance Fees / Total People in the Family
Entrance Fee Per Person =56/4
Entrance Fee Per Person = [B]14[/B]

a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. W

a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. WRITE A LINEAR FUNCTION IN THE FORM Y=MX+B, FOR THE TOTAL COST OF GOING TO THE BASEBALL GAME,Y, AND THE TOTAL NUMBER PEOPLE IN THE FAMILY,X.
We have:
[B]y = 21x + 5[/B]
Since the cost of each ticket is $21, we multiply this by x, the total number of people in the family.
We add 5 as the cost to park the car, which fits the entire family, and is a one time cost.

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at a profit of 4 per pig. His total profit was $56. How many pigs did he originally buy?
Let p be the purchase price of pigs. We're given:
[LIST]
[*]Farmer originally bought [I]p [/I]pigs for 232 which is our cost C.
[*]5 of them died, so he has p - 5 left
[*]He sells 4(p - 5) pigs for a revenue amount R
[*]Since profit is Revenue - Cost, which equals 56, we have:
[/LIST]
Calculate Profit
P = R - C
Plug in our numbers:
4(p - 5) - 232 = 56
4p - 20 - 232 = 56
To solve for p, [URL='https://www.mathcelebrity.com/1unk.php?num=4p-20-232%3D56&pl=Solve']we type this equation into our search engine[/URL] and we get:
p = [B]77[/B]

A farmer has a total of 200 ducks and cows in his barn. If he has n cows, how many total legs are th

A farmer has a total of 200 ducks and cows in his barn. If he has n cows, how many total legs are there in the barn? (Make sure you include the farmer.)
[LIST]
[*]Number of cows = n
[*]Legs per cow = 4
[*]Cows legs = 4n
[*]Number of ducks = 200 - n
[*]Legs per duck = 2
[*]Number of ducks legs = (200 - n) x 2 = 400 - 2n
[*]Farmers legs = 2
[/LIST]
Total legs = Cows legs + Ducks Legs + Farmers Legs
Total legs = 4n + 400 - 2n + 2
Total legs = [B]2n + 402[/B]

A farmer has c chickens. She sells 3 of them for $6 each and the rest she sells for $5 each. How muc

A farmer has c chickens. She sells 3 of them for $6 each and the rest she sells for $5 each. How much money will she receive?
Total money received = 3 * 6 + 5(c - 3)
Total money received = 18 + 5c - 15
Total money received = [B]5c + 3[/B]

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his l

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his land to grow green beans. He uses the remaining 7 acres to grow wheat.How many total acres does the farmer own?
Convert all land portions to fractions or decimals. We will do fractions:
[LIST]
[*]1/3 for corn
[*][I]A quarter[/I] means 1/4 for lettuce
[*]12.5% is 12.5/100 or 1/8 for green beans
[/LIST]
Now add all these up:
1/3 + 1/4 + 1/8
We need a common factor for 3, 4, and 8. Using our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=3&num2=4&num3=8&pl=LCM']LCM Calculator[/URL], we get 24.
1/3 = 8/24
1/4 = 6/24
18 = 3/24
Add them all up:
(8 + 6 + 3)/24
17/24
This means 17/24 of the land is used for everything but wheat. Wheat occupies (24-17)/24 = 7/24 of the land.
We'll use a for the number of acres on the farm.
7a/24 = 7
[B]a = 24[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 29. F

A first number plus twice a second number is 10. Twice the first number plus the second totals 29. Find the numbers.
Let the first number be x. Let the second number be y. We are given the following two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 29
[/LIST]
We can solve this 3 ways using:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Substitution']Substitution[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Elimination']Elimination[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
Using any of the 3 methods, we get the same answers of [B](x, y) = (16, -3)[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. F

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers.
[U]The phrase [I]a number[/I] means an arbitrary variable[/U]
A first number is written as x
A second number is written as y
[U]Twice a second number means we multiply y by 2:[/U]
2y
[U]A first number plus twice a second number:[/U]
x + 2y
[U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U]
x + 2y = 10
[U]Twice the first number means we multiply x by 2:[/U]
2x
[U]Twice the first number plus the second:[/U]
2x + y
[U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U]
2x + y = 35
Therefore, we have a system of two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 35
[/LIST]
Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -20
[*]2x + y = 35
[/LIST]
Because the x variables are opposites, we can add both equations together:
(-2 + 2)x + (-4 + 1)y = -20 + 35
The x terms cancel, so we have:
-3y = 15
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-5
[/B]
Now we substitute this y = -5 into equation 2:
2x - 5 = 35
To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get:
x = [B]20[/B]

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. F

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. Find the numbers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x + 2y = 11
[*]2x + y = 34
[/LIST]
Using our simultaneous equations calculator, we have 3 methods to solve this:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
All 3 methods give the same solution:
[LIST]
[*][B]x = 19[/B]
[*][B]y = -4[/B]
[/LIST]

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. F

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers.
[B][U]Givens and assumptions:[/U][/B]
[LIST]
[*]Let the first number be x.
[*]Let the second number be y.
[*]Twice means multiply by 2
[*]The phrases [I]is[/I] and [I]totals[/I] mean equal to
[/LIST]
We're given two equations:
[LIST=1]
[*]x + 2y = 14
[*]2x + y = 40
[/LIST]
To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system:
[LIST=1]
[*]-2x - 4y = -28
[*]2x + y = 40
[/LIST]
Now add both equations together
(-2 _ 2)x (-4 + 1)y = -28 + 40
-3y = 12
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D12&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-4
[/B]
We substitute this back into equation 1 for y = -4:
x + 2(-4) = 14
x - 8 = 14
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-8%3D14&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]22[/B]

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. F

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + 2y = 22 <-- Since twice means multiply by 2
[*]2x + y = 28 <-- Since twice means multiply by 2
[/LIST]
We have a set of simultaneous equations. We can solve this three ways
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28+&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*][B]x = 11 & 1/3[/B]
[*][B]y = 5 & 1/3[/B]
[/LIST]

A first number plus twice a second number is 3. Twice the first number plus the second totals 24.

A first number plus twice a second number is 3. Twice the first number plus the second totals 24.
Let the first number be x. Let the second number be y. We're given:
[LIST=1]
[*]x + 2y = 3 <-- Because [I]twice[/I] means multiply by 2
[*]2x + y = 24 <-- Because [I]twice[/I] means multiply by 2
[/LIST]
We have a system of equations. We can solve it any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which way we choose, we get:
[LIST]
[*]x = [B]15[/B]
[*]y = [B]-6[/B]
[/LIST]

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Fi

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + 2y = 6
[*]2x + y = 15
[/LIST]
Multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -12
[*]2x + y = 15
[/LIST]
Now add them
-2x + 2x - 4y + y = -12 + 15
-3y = 3
Divide each side by -3:
y = 3/-3
y =[B] -1[/B]
Plug this back into equation 1:
x + 2(-1) = 6
x - 2 = 6
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-2%3D6&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]8[/B]

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Fi

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers
Let the first number be a and the second number be b. We have:
[LIST=1]
[*]a + 2b = 7
[*]2a + b = 23
[/LIST]
Rearrange (1) into (3)
(3) a = 7 - 2b
Substitute (3) into (2):
2(7 - 2b) + b = 23
Multiply through:
14 - 4b + b = 23
Combine like terms:
14 - 3b = 23
Subtract 14 from each side:
-3b = 9
Divide each side by -3
[B]b = -3[/B]
Substitute this into (3)
a = 7 - 2b
a = 7 - 2(-3)
a = 7 + 6
[B]a = 13[/B]
[B](a, b) = (13, -3)[/B]

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from sel

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?
Let the number of drinks be d. Let the number of salads be s. We're given two equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d + s = 209
[/LIST]
We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides:
d + s - s = 209 - s
Cancel the s's, we get:
d = 209 - s
So we have the following system of equations:
[LIST=1]
[*]2d + 6.50s = 836.50
[*]d = 209 - s
[/LIST]
Substitute equation (2) into equation (1) for d:
2(209 - s) + 6.50s = 836.50
Multiply through to remove the parentheses:
418 - 2s + 6.50s = 836.50
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]:
s = [B]93[/B]

A football gained 52 yards during the possession. In the next 3 possessions they gained the same amo

A football gained 52 yards during the possession. In the next 3 possessions they gained the same amount of yards each time. If they gained a total of 256 yards, write and solve an equation for how many yards they gained in each of the last 3 possessions.
Subtract 52 initial yards
256 - 52 = 204
Now, divide 204 by 3 possessions
204/3 = [B]68 yards[/B]

A football team loses 27 yards total during its first 3 plays. On average, what is the yards per pl

A football team loses 27 yards total during its first 3 plays. On average, what is the yards per play for these 3 plays?
A loss of yards means negative yardage.
Average Yards per play = Total Yards / Total plays
Average Yards per play = -27/3
Average Yards per play = -[B]9 or 9 yard loss[/B]

A football team lost 7 yards each play for four consecutive plays. Represent the team’s total change

A football team lost 7 yards each play for four consecutive plays. Represent the team’s total change in position for the four plays as an integer.
A net loss in yardage for 7 yards is written as -7
4 plays * -7 yards equals [B]-28[/B]

A fruit basket contains 2 red apples and 2 green apples. What is the ratio of the number of red appl

A fruit basket contains 2 red apples and 2 green apples. What is the ratio of the number of red apples to the total number of apples?
2:2 = [B]1:1[/B] simplified

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at eac

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at each store it opens. Let s represent the number of stores and m represent the total number of employees.
There is only one corporate headquarters. So we have the number of employees (m) as:
m = Store Employees + Corporate Employees
Each store has 25 employees. Total store employees equal 25 per store times the number of stores (s).
[B]m = 25s + 25[/B]

A game show has 74 categories. There are 9,785 points in each category. How many points are there in

A game show has 74 categories. There are 9,785 points in each category. How many points are there in total on the game show?
Total points = Total categories * points per category
Total points = 9785 * 74
Total points = [B]724,090[/B]

A girl bought a skirts at $30 each and j jerseys at $15 each at a total cost of $285.

A girl bought a skirts at $30 each and j jerseys at $15 each at a total cost of $285.
Since cost = price * quantity, we have:
[B]30a + 15j = 285[/B]

A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A balls, 4 type B

A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A balls, 4 type B balls, and 9 type C balls, find the probability that the golf ball is not a type A ball
Not Type A means Type B or Type C.
Our total balls = 5 + 4 + 9 = 18
P(B or C) = P(B) + P(C)
P(B or C) = 4/18 + 9/18
P(B or C) = [B]13/18[/B]

A group of 30 students from your school is part of the audience for a TV game show. The total number

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120. What theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots?
We want the probability a student from your school is chosen out of total students times total ways to choose students from your school:
[U]a) P(5 students being selected):[/U]
5/30 * 4/(120 - 30)
5/30 * 4/90
20/2700
[URL='https://www.mathcelebrity.com/fraction.php?frac1=20%2F2700&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
1/135
[U]b) Total Ways 9 students can be picked from your school:[/U]
9/120
[URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F120&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get:
3/40
Divide a by b:
1/135 / 3/40
40/405
[URL='https://www.mathcelebrity.com/fraction.php?frac1=40%2F405&frac2=3%2F8&pl=Simplify']Simplifying[/URL], we get:
[B]8/81[/B]

A group of 4 adults and 5 children is visiting an amusement park. Admission is $15 per adult and $9

A group of 4 adults and 5 children is visiting an amusement park. Admission is $15 per adult and $9 per child. Find the total cost of admission for the group.
Set up the cost function for adults and children:
C(a, c) = 15a + 9c
We want the cost for 4 adults and 5 children
C(4, 5) = 15(4) + 9(5)
C(4, 5) = 60 + 45
C(4, 5) = [B]105[/B]

A group of people were asked if they had run a red light in the last year. 497 responded "yes", and

A group of people were asked if they had run a red light in the last year. 497 responded "yes", and 223 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year.
P(Run Red Light) = yes answers / total answers
P(Run Red Light) = 497 / (497 + 223)
P(Run Red Light) = 497 / 720
P(Run Red Light) = [B]0.6903[/B]

A group of workers can plant 72 acres in 8 days what is the rate in acres per a day

A group of workers can plant 72 acres in 8 days what is the rate in acres per a day
Acres per day = Total Acres / Total Days
Acres per day = 72/8
Acres per day =[B] 9[/B]

A guitar that normally cost n dollars is on sale for 20% off. The tax is 8%. What is the total cost

A guitar that normally cost n dollars is on sale for 20% off. The tax is 8%. What is the total cost of the guitar including tax?
Discount Amount = 0.2n
Total paid after discount = n - 0.2n = 0.8n
Tax amount:
0.8n * 0.08 = 0.064n
After tax amount:
0.8n + 0.64n = [B]0.864n[/B]

A gym charges a $30 sign-up fee plus $20 per month. You have a $130 gift card for the gym. When doe

A gym charges a $30 sign-up fee plus $20 per month. You have a $130 gift card for the gym. When does the total spent on your gym membership exceed the amount of your gift card?
Subtract the sign up fee of $30 from your gift card amount:
$130 - $30 = $100
Since each month costs $20, we have $100/$20 = 5 months.
So if you go for [B]more than 5 months[/B], you'll exceed your gift card.

A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to rep

A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to represent the total number of students s taking yoga.
Total students is the number of classes times the number of students in each class:
[B]s = 11c[/B]

A gym has yoga classes. Each class has 14 students. If there are c classes write an equation to repr

A gym has yoga classes. Each class has 14 students. If there are c classes write an equation to represent the total number of students s taking yoga
s = students per class * number of classes
[B]s = 14c[/B]

A hexagon has a total 126 dots and a equal number of dots on each side. how many dots on each side?

A hexagon has a total 126 dots and a equal number of dots on each side. how many dots on each side?
Since it has an equal number of dots on each side, each side has:
Number of dots on each side = 126 dots / 6 sides
Number of dots on each side = [B]21 dots per side[/B]

A house rental company charges a $700 for a week stay plus an additional $4 per night for a roll awa

A house rental company charges a $700 for a week stay plus an additional $4 per night for a roll away bed. Your family rents a house for a week and pays $756. How many roll away beds did they rent?
Roll Away Beds = (Total Rental Price - Weekly Charge)/Per night bed fee
Plugging in our numbers, we get:
Roll Away Beds = (756 - 700)/4
Roll Away Beds = 56/4
Roll Away Beds = [B]14[/B]

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 jar contains 7 red marbles, 8 green marbles, and 6 blue marbles. What is the probability that you

A jar contains 7 red marbles, 8 green marbles, and 6 blue marbles. What is the probability that you draw 4 green marbles in a row if you do not replace the marbles after each draw?
The key phrase in this problem is [I]do not replace[/I].
[U]Draw #1:[/U]
P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar
Total Green Marbles in the Jar = 8
Total Marbles in the Jar = 7 red + 8 green + 6 blue = 21
P(Green) = 8/21
[U]Draw #2:[/U]
P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar
Total Green Marbles in the Jar = 8 - 1 = 7
Total Marbles in the Jar = 7 red + 7 green + 6 blue = 20
P(Green) = 7/20
[U]Draw #3:[/U]
P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar
Total Green Marbles in the Jar = 7 - 1 = 6
Total Marbles in the Jar = 7 red + 6 green + 6 blue = 19
P(Green) = 6/19
[U]Draw #4:[/U]
P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar
Total Green Marbles in the Jar = 6 - 1 = 5
Total Marbles in the Jar = 7 red + 5 green + 6 blue = 18
P(Green) = 5/18
We want P(Green, Green, Green, Green)
Because each draw is [U][B]independent[/B][/U] of all other draws, we multiply each draw to get the final probability
P(Green, Green, Green, Green) = P(Green on Draw 1) * P(Green on Draw 2) * P(Green on Draw 3) * P(Green on Draw 4) *
P(Green, Green, Green, Green) = 8/21 * 7/20 * 6/19 * 5/18
P(Green, Green, Green, Green) = 1680/143640
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1680%2F143640&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we get:
P(Green, Green, Green, Green) = [B]2/171
[MEDIA=youtube]b2C_D4_d0Ug[/MEDIA][/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 kilo of grapes costs 200.50 how much will you pay if you buy 3 kilos

a kilo of grapes costs 200.50 how much will you pay if you buy 3 kilos
Total Amount = Cost per unit * Quantity
Total Amount = 200.50 * 3
Total Amount = [B]$601.50[/B]

A kilogram of chocolate costs8 dollars. Sally buys p kilograms. Write an equation to represent the t

A kilogram of chocolate costs8 dollars. Sally buys p kilograms. Write an equation to represent the total cost c that Sally pays.
c[B] = 8p[/B]

A kilogram of rice costs $2.05.what is the cost of 30kg of the rice?

A kilogram of rice costs $2.05.what is the cost of 30kg of the rice?
We multiply the price for 1 kilogram by the 30 kilograms total:
$2.05 * 30 = [B]$61.50[/B]

A large bag of candy contains 84 blue candies, 96 red candies, and 120 yellow candies. What percent

A large bag of candy contains 84 blue candies, 96 red candies, and 120 yellow candies. What percent of the candies are red?
[U]Calculate total candies:[/U]
Total Candies = Blue Candies + Red Candies + Yellow Candies
Total Candies = 84 + 96 + 120
Total Candies = 300
[U]Now calculate the red candy percentage:[/U]
Red Candy Percent = 100 * Red Candies / Total Candies
Red Candy Percent = 100 * 96 / 300
Red Candy Percent = 9600 / 300
Red Candy Percent = [B]32%[/B]

A lead pipe 20 ft long is 3/8 inch thick and has an inner diameter of 3 inches. Find the volume of l

A lead pipe 20 ft long is 3/8 inch thick and has an inner diameter of 3 inches. Find the volume of lead in it.
A lead pipe is a cylinder. We want the volume of a cylinder.
Convert 20ft to inches:
20ft = 12(20) = 240 inches
Find the inner radius:
1/2 * inner diameter
1/2 * 3 = 3/2
Now add the thickness for the total radius
3/2 + 3/8 = 12/8 + 3/8 = 15/8
Find volume of the lead where volume = pi r^2 h
Lead vol (V) = Overall volume - inner volume
Lead Vol = pi(15/8)^2(240) - pi(3/2)^2(240)
Lead Vol = 240pi(225/64 - 9/4)
9/4 = 144/64
Lead Vol = 240pi(225/64 - 144/64)
Lead Vol = 240pi(81/64)
[B]Lead Vol = 303.75pi[/B]

A license plate is made up of 2 letter and 3 single digit numbers

A license plate is made up of 2 letter and 3 single digit numbers.
There are 26 letters (A-Z). And there are 10 single digit numbers [0-9]. So our total combinations are:
Letter - Letter - Number - Number - Number
26 * 26 * 10 * 10 * 10 = [B]676,000[/B]

A limo costs $85 to rent for 3 hours plus a 7% sales tax. What is the total cost to rent the limo fo

A limo costs $85 to rent for 3 hours plus a 7% sales tax. What is the total cost to rent the limo for 6 hours?
Determine the number of 3 hour blocks:
3 hour blocks = Total Rental Time / 3
3 hour blocks = 6 hours / 3
3 hour blocks = 2
With 7% = 0.07, we have:
Total Cost = $85 * / 3 hours * 2 (3 hour blocks) * 1.07
Total Cost = 85 * 2 * 1.07
Total Cost = [B]181.9[/B]

A loaf of bread has 35 slices. Ann eats 8 slices, Betty eats 6 slices, Carl eats 5, and Derrick eats

A loaf of bread has 35 slices. Ann eats 8 slices, Betty eats 6 slices, Carl eats 5, and Derrick eats 9 slices. What fraction of the loaf is left?
[U]Calculate total slices eaten:[/U]
Slices eaten = Ann + Betty + Carl + Derrick
Slices eaten = 8 + 6 + 5 + 9
Slices eaten = 28
[U]Calculate remaining slices:[/U]
Remaining slices = Slices in loaf - Slices Eaten
Remaining slices = 35 - 28
Remaining slices = 7
[U]Calculate fraction of the loaf left:[/U]
Fraction left = Remaining Slices / Slices in Loaf
Fraction left = 7/35
We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=7%2F35&frac2=3%2F8&pl=Simplify']type 7/35 into our search engine[/URL], choose simplify, and we get:
Fraction left = [B]1/5[/B]

A local college classifies its students by major, year (Freshman, Sophomore, Junior, Senior) and sex

A local college classifies its students by major, year (Freshman, Sophomore, Junior, Senior) and sex (M, F). If the college offers 20 majors, how many combinations are possible?
We have 20 majors, 4 grade levels, and 2 sexes.
The total combinations = 20 * 4 * 2 = [B]160[/B]

A local radio station sells time slots for programs in 20-minute intervals. If the station operates

A local radio station sells time slots for programs in 20-minute intervals. If the station operates 24 hours per day, what is the total number of 20-minute time slots the radio station can sell for Thursday and Friday?
Thursday and Friday = 2 days
With 24 hours per day, we have 24 * 2 = 48 hours for Thursday and Friday.
Since 20 minutes is 1/3 of an hour, then we have 3 20-minute time slots per hour.
3 20-minute time slots * 48 hours = [B]144[/B] total 20-minute time slots

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a p

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a person buys 1 ticket for $5.
Set up the expected values E(x):
for the 1,000 price:
E(x) = (1000 - 5) * 1/1000 = 995/1000
For the 5 $100 prizes:
E(x) = (100 - 5) * 5/1000 = 475/1000
For the losing ticket. With 6 winning tickets, we have 1000 - 6 = 994 losing tickets:
E(x) = -3 * 994/1000 = -2982/1000
We get our total expected value by adding all of these expected values up. Since they all have the same denominator, we add numerators:
E(x) = (995 + 475 - 2982)/1000
E(x) = -1512/1000
E(x) = [B]-1.51[/B]

A luncheon for 14 guests cost $468.00. What was the average cost per guest?

A luncheon for 14 guests cost $468.00. What was the average cost per guest?
Average Cost per Guest = Total Cost / Number of Guests
Average Cost per Guest = $468 / 14
Average Cost per Guest = [B]$33.43[/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 invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments

A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=5200&i1=4&i2=3&itot=194&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1 = $3,800[/B]
[*][B]Fund 2 = $1,400[/B]
[/LIST]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket?
Declare variables:
[LIST]
[*]Let a be the number of adult's tickets
[*]Let c be the number of children's tickets
[/LIST]
Cost = Price * Quantity
We're given two equations:
[LIST=1]
[*]a + c = 20
[*]15a + 10c = 225
[/LIST]
Rearrange equation (1) in terms of a:
[LIST=1]
[*]a = 20 - c
[*]15a + 10c = 225
[/LIST]
Now that I have equation (1) in terms of a, we can substitute into equation (2) for a:
15(20 - c) + 10c = 225
Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225
We first need to simplify the expression removing parentheses
Simplify 15(20 - c): Distribute the 15 to each term in (20-c)
15 * 20 = (15 * 20) = 300
15 * -c = (15 * -1)c = -15c
Our Total expanded term is 300-15c
Our updated term to work with is 300 - 15c + 10c = 225
We first need to simplify the expression removing parentheses
Our updated term to work with is 300 - 15c + 10c = 225
[SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE]
(-15 + 10)c = -5c
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
-5c + 300 = + 225
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 300 and 225. To do that, we subtract 300 from both sides
-5c + 300 - 300 = 225 - 300
[SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE]
-5c = -75
[SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE]
-5c/-5 = -75/-5
c = [B]15[/B]
Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a:
a = 20 - 15
a = [B]5[/B]

A marathon runner took 2 hours and 15 minutes to complete the race. During that time he spent 50 min

A marathon runner took 2 hours and 15 minutes to complete the race. During that time he spent 50 minutes in the lead. Write down, in its simplest form, the fraction of time he spent in the lead.
[U]Calculate total race time in minutes[/U]
[URL='https://www.mathcelebrity.com/timecon.php?quant=2&pl=Calculate&type=hour']2 hours[/URL] = 120 minutes
120 minutes + 15 minutes = 135 minutes
[U]Calculate fraction of lead time[/U]
Fraction of lead time = Time spent in lead / total race time
Fraction of lead time = 50/135
Simplifying this fraction, we get:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=50%2F135&frac2=3%2F8&pl=Simplify']Fraction of lead time[/URL] = [B]10/27[/B]

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechan

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechanic works h hours.
Set up the cost function C(h) where h is the number of hours worked:
C(h) = Hourly Rate * h + parts
C(h) = [B]45h + 125[/B]

A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechani

A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechanic a total of $310. Write and solve an equation to find the amount of time h (in hours) the mechanic works on your heater.
We calculate the cost function C(h) as:
C(h) = Hourly Rate * hours + Flat Fee Inspection
C(h) = 80h + 50 <-- this is our cost equation
Now, we want to solve for h when C(h) = 310
80h + 50 = 310
[URL='https://www.mathcelebrity.com/1unk.php?num=80h%2B50%3D310&pl=Solve']We type this equation into our search engine[/URL] and we get:
h = [B]3.25[/B]

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended. What is the maximum number of events someone can attend for a total cost of $47?
Subtract the join fee from the total cost:
$47 - $16 = $31
Now divide this number by the cost per event:
$31 / $1 = [B]31 events[/B]

A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an

A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an admission the total receipts were 1228 how many were seniors and how many were adults?
Let the number of adult tickets be a. Let the number of senior tickets be s. We're given two equations:
[LIST=1]
[*]a + s = 324
[*]7a + 3s = 1228
[/LIST]
We have a set of simultaneous equations we can solve using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]a = 64[/B]
[*][B]s = 260[/B]
[/LIST]

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid for admission, the total receipt were 1118. How many who paid were adults ? How many were senior citizens?
Let a be the number of adult tickets. Let s be the number of senior citizen tickets. We're given two equations:
[LIST=1]
[*]a + s = 304
[*]7a + 2s = 1118
[/LIST]
We can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Cramers+Method']Cramer's Method[/URL]
[/LIST]
No matter which way we choose, we end up with the same answer:
[LIST]
[*]a = [B]102[/B]
[*]s = [B]202[/B]
[/LIST]

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for stu

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1030, How many children, students, and adults attended?
Let c be the number of children's tickets, s be the number of student's tickets, and a be the number of adult's tickets. We have 3 equations:
[LIST=1]
[*]a + c + s = 143
[*]a = 0.5c
[*]12a + 5c + 7s =1030
[/LIST]
Substitute (2) into (1)
0.5c + c + s = 143
1.5c + s = 143
Subtract 1.5c from each side
4. s = 143 - 1.5c
Now, take (4) and (2), and plug it into (3)
12(0.5c) + 5c + 7(143 - 1.5c) = 1030
6c + 5c + 1001 - 10.5c = 1030
Combine like terms:
0.5c + 1001 = 1030
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.5c%2B1001%3D1030&pl=Solve']equation calculator[/URL] to get [B]c = 58[/B].
Plug this back into (2)
a = 0.5(58)
[B]a = 29
[/B]
Now take the a and c values, and plug it into (1)
29 + 58 + s = 143
s + 87 = 143
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B87%3D143&pl=Solve']equation calculator[/URL] again, we get [B]s = 56[/B].
To summarize, we have:
[LIST]
[*]29 adults
[*]58 children
[*]56 students
[/LIST]

A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear eq

A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear equation to find the total cost to download 30 songs
Set up the cost function C(s) where s is the number of songs:
C(s) = cost per song * s + download fee
Plugging in our numbers for s = 30 and a download fee of $2 and s = 1.29, we have:
C(30) = 1.29(30) + 2
C(30) = 38.7 + 2
C(30) = [B]40.7[/B]

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear equation to find the total cost to download 30 songs.
Let the number of songs be s. And the cost function be C(s). We have:
C(s) = Price per song downloaded * s + app download charge
C(s) = 1.29s + 2
The problem asks for C(30):
C(3) = 1.29(30) + 2
C(3) = 38.7 +2
C(3) = $[B]40.7[/B]

A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equa

A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equation and a linear equation to find the total cost to download 30 songs
Set up the equation C(d) where d is the number of downloads:
C(d) = cost per download * d + download fee
Plugging in our numbers, we get:
C(d) = 1.29d + 2
The problem asks for C(30):
C(30) = 1.29(30) + 2
C(30) = 38.7 + 2
C(30) = [B]40.70[/B]

A necklace chain costs $15. Beads cost $2.75 each. You spend a total of $28.75 on a necklace and bea

A necklace chain costs $15. Beads cost $2.75 each. You spend a total of $28.75 on a necklace and beads before tax. How many beads did you buy in addition to the necklace?
[U]Calculate the amount left to spend on beads:[/U]
Bead Spend = Total Spend - Necklace Cost
Bead Spend = $28.75 - $15
Bead Spend = $13.75
[U]Calculate the number of beads you bought:[/U]
Beads Bought = Bead Spend / Cost Per Bead
Beads Bought = $13.75 / $2.75
Beads Bought = [B]$5[/B]

A pack of 12 tortillas cost $3.24. What is the price per tortilla?

A pack of 12 tortillas cost $3.24. What is the price per tortilla?
Price per tortilla = Total Cost / Total Tortillas
Price per tortilla = $3.24/12
Price per tortilla = [B]$0.27[/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 packing machine can package 236 first aid kit each hour. At this rate, find the number of first ai

A packing machine can package 236 first aid kit each hour. At this rate, find the number of first aid kit package in 24 hours
Total First Aid Kits = Kits Per Hour * Number of Hours
Total First Aid Kits = 236 * 24
Total First Aid Kits = [B]5,664[/B]

A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84.

A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84. What was the rental cost per hour?
9am to 4pm is 7 hours.
Cost per hour = Total Cost / Hours
Cost per hour = 28.84 / 7
Cost per hour = [B]$4.12[/B]

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh of his route, how many papers does he deliver
Let d be the total number of deliveries the paper boy makes on the route.
d
We're given, d/7 = 13
d = 13 * 7
d = [B]91
[MEDIA=youtube]HRviz-3fn5c[/MEDIA][/B]

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $37. The total cost to rent 2 chairs and 6 tables is $64. What is the cost to rent each chair and each table?
Let c be the cost of renting one chair and t be the cost of renting one table. We're given two equations:
[LIST=1]
[*]5c + 3t = 37
[*]2c + 6t =64
[/LIST]
We have a system of equations. Using our system of equations calculator, we can solve this problem any of 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
All 3 methods give the same answer:
[LIST]
[*][B]Chairs (c) cost $1.25[/B]
[*][B]Tables (t) cost $10.25[/B]
[/LIST]

A person is earning 600 per day to do a certain job. Express the total salary as a function of the n

A person is earning 600 per day to do a certain job. Express the total salary as a function of the number of days that the person works.
Set up the salary function S(d) where d is the number of days that the person works:
S(d) = Daily Rate * d
[B]S(d) = 600d[/B]

A playground requires 2,459 pounds of sand to cover the ground. If the sand comes in 60-pound bags,

A playground requires 2,459 pounds of sand to cover the ground. If the sand comes in 60-pound bags, how many bags are needed
Number of bags = Total Weight of Sand / Pounds per bag
Number of bags = 2459/60
Number of bags = 40.9833

A pound of chocolate costs 6 dollars. Greg buys p pounds. Write an equation to represent the total c

A pound of chocolate costs 6 dollars. Greg buys p pounds. Write an equation to represent the total cost c that Greg pays
Since cost = price * quantity, we have:
[B]c = 6p[/B]

A pound of chocolate costs 6 dollars. Ryan buys p pounds. Write an equation to represent the total c

A pound of chocolate costs 6 dollars. Ryan buys p pounds. Write an equation to represent the total cost c that Ryan pays
Since cost = Price * Quantity, we have:
[B]c = 6p[/B]

A pound of chocolate costs 7 dollars. Hong buys p pounds . Write an equation to represent the total

A pound of chocolate costs 7 dollars. Hong buys p pounds . Write an equation to represent the total cost c that Hong pays
Our equation is the cost of chocolate multiplied by the number of pounds:
[B]c = 7p[/B]

A property sold for $198,000 with a listing commission of 8%. The selling office is to receive 40% o

A property sold for $198,000 with a listing commission of 8%. The selling office is to receive 40% of the total commission. How much will the listing salesperson receive if she is paid 60% of the amount retained by listed broker.
[U]Calculate commission amount:[/U]
Commission amount = Sale Price * Commission Percent
Commission amount = 198,000 * 8%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=8&den1=198000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Commission amount [/URL]= 15,840
[U]Calculate listing salesperson commission amount:[/U]
Listing salesperson commission amount = Commission Amount * Listing salesperson Percent
Listing salesperson commission amount = 15,840 * 60%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=15840&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Listing salesperson commission amount[/URL] = [B]9,504[/B]

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the learners in the class have black hair. How many learners in the class if 9 of them have blonde hair?
Total learners = Blond + Brown + Black
Total Learners = 1/4 + 2/3 + Black
Total Learners will be 1, the sum of all fractions
1/4 + 2/3 + Black = 1
Using common denominators of 12, we have:
3/12 + 8/12 + Black = 12/12
11/12 + Black = 12/12
Subtract 11/12 from each side:
Black = 1/12
Let t be the total number of people in class. We are given for blondes:
1/4t = 9
Multiply each side by 4
[B]t = 36[/B]
Brown Hair
2/3(36) = 24
Black Hair
1/12(36) = 3

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afte

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).
Checkout Time (in minutes) | Frequency | Relative Frequency
1.0 - 1.9 | 2 | ?
2.0 - 2.9 | 8 | ?
3.0 - 3.9 | ? | ?
4.0 - 5.9 | 5 | ?
Total | 25 | ?
(a) Complete the frequency table with frequency and relative frequency.
(b) What percentage of the checkout times was less than 3 minutes?
(c)In what class interval must the median lie? Explain your answer.
(d) Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why?
(a)
[B]Checkout Time (in minutes) | Frequency | Relative Frequency
1.0 - 1.9 | 2 | 2/25
2.0 - 2.9 | 8 | 8/25
3.0 - 3.9 | 10 (since 25 - 5 + 8 + 2) = 10 | 10/25
4.0 - 5.9 | 5 | 5/25
Total | 25 | ?[/B]
(b) (2 + 8)/25 = 10/25 = [B]40%[/B]
c) [B]3.0 - 3.9[/B] since 2 + 8 + 10 + 5 = 25 and 13 is the middle value which occurs in the 3.0 - 3.9 interval
(d) [B]Mean increases[/B] since it's a higher value than usual. Median would not change as the median is the most frequent distribution and assuming the 5.8 is only recorded once.

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remai

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remainder. How much commission is received on the sale of a $450,000 property?
Calculate commission on first $100,000 (Commission 1):
Commission 1 = $100,000 * 0.035
Commission 1 = $3,500
Calculate commission on the remainder (Commission 2):
Commission 2 = 0.025 * ($450,000 - $100,000)
Commission 2 = 0.025 * ($350,000)
Commission 2 = $8,750
Calculate Total Commission:
Total Commission = Commission 1 + Commission 2
Total Commission = $3,500 + $8,750
Total Commission = [B]$12,250[/B]

A realtor makes an annual salary of $25000 plus a 3% commission on sales. If a realtor's salary is $

A realtor makes an annual salary of $25000 plus a 3% commission on sales. If a realtor's salary is $67000, what was the amount of her sales?
Total post-salary pay = $67,000 - $25,000 = $42,000
Let Sales be s.
So 0.03s = $42,000
Divide each side by 0.03
s = $1,400,000

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room wi

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room with carpet that costs $76.00 per square yard. How much will it cost to recarpet the room? $
The area of a rectangle is length * width, so we have:
A = 5 yards * 4 yards
A = 20 square yards
Total cost = Cost per square yard * total square yards
Total Cost = $76 * 20
Total Cost = [B]$1520[/B]

A repair will require 3 hours at $40 per hour. How much will the total/labor cost be for this job?

A repair will require 3 hours at $40 per hour. How much will the total/labor cost be for this job?
Total cost = Hourly Labor Rate * hours
Total cost = $40 * 3
Totaal cost = [B]$120[/B]

A restaurant bill comes to $28.35. Find the total cost if the tax is 6.25% and a 20% tip is left on

A restaurant bill comes to $28.35. Find the total cost if the tax is 6.25% and a 20% tip is left on the amount before tax.
Calculate the tip:
Tip = Bill Before Tax * Tip %
Tip = $28.35 * 20%
Tip = $5.67
Calculate Tax:
Tax = Bill without Tip * Tax %
Tax = $28.35 * 6.25%
Tax = $1.77
Total Cost = Bill + Tax + Tip
Total Cost = $28.35 + $5.67 + $1.77
Total Cost = [B]$35.79[/B]

A restaurant is open for 10 ½ hours during the day. The restaurant has 5 ½ families coming and leavi

A restaurant is open for 10 ½ hours during the day. The restaurant has 5 ½ families coming and leaving every hour. A family has 4 members. How many people have visited the restaurant during the day?
[U]Given:[/U]
[LIST]
[*]10 & 1/2 = 10.5 hours
[*]5 & 1/2 = 5.5 families
[/LIST]
Total Visitors = Hours Open * Families per hour * member per family
Total Visitors = 10.5 * 5.5 * 4
Total Visitors = [B]231[/B]

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplif

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplify an expression including units to find the total number of people that can ride the roller coaster at one time
6 trains * 3 cars per train * 4 people per car = [B]72 people[/B]

A sales clerk receives a monthly salary of $750 plus a commission of 4% on all sales over $3900. Wha

A sales clerk receives a monthly salary of $750 plus a commission of 4% on all sales over $3900. What did the clerk earn the month that she sold $12,800 in merchandise?
[U]Calculate Commission Sales Eligible Amount:[/U]
Commission Sales Eligible Amount = Sales - 3900
Commission Sales Eligible Amount = 12800 - 3900
Commission Sales Eligible Amount = 8900
[U]Calculate Commission Amount:[/U]
Commission Amount = Commission Sales Eligible Amount * Commission Percent
Commission Amount = [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=4&den1=8900&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']8900 * 4%[/URL]
Commission Amount = 356
[U]Calculate total earnings:[/U]
Total Earnings = Base Salary + Commission Amount
Total Earnings = 750 + 356
Total Earnings = [B]1106[/B]

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,0

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,000. If x represents the salesperson’s weekly sales, express the total weekly earnings E(x) as a function of x and simplify the expression. Then find E(2,000) and E(7,000) and E(10,000).
15% as a decimal is written as 0.15.
Build our weekly earnings function
E(x) = Commission + Base Salary
E(x) = 0.15(Max(0, x - 5000)) + 300
Now find the sales salary for 2,000, 7,000, and 10,000 in sales
E(2,000) = 0.15(Max(0,2000 - 5000)) + 300
E(2,000) = 0.15(Max(0,-3000)) + 300
E(2,000) = 0.15(0) + 300
[B]E(2,000) = 300
[/B]
E(7,000) = 0.15(Max(0,7000 - 5000)) + 300
E(7,000) = 0.15(Max(0,2000)) + 300
E(7,000) = 0.15(2,000) + 300
E(7,000) = 300 + 300
[B][B]E(7,000) = 600[/B][/B]
E(10,000) = 0.15(Max(0,10000 - 5000)) + 300
E(10,000) = 0.15(Max(0,5000)) + 300
E(10,000) = 0.15(5,000) + 300
E(10,000) = 750+ 300
[B][B]E(10,000) = 1,050[/B][/B]

A school bus can safely carry as many as 76 students. If 19 students are already on the bus, how man

A school bus can safely carry as many as 76 students. If 19 students are already on the bus, how many more can board the bus?
Remaining boarders = total capacity - students on the bus
Remaining boarders = 76 - 19
Remaining boarders = [B]57[/B]

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 f

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
We want combinations for freshmen, sophomores, juniors, and seniors.
[LIST]
[*]Freshmen choices: [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=2&pl=Combinations']6 C 2[/URL] = 15
[*]Sophomore choices: [URL='https://www.mathcelebrity.com/permutation.php?num=9&den=3&pl=Combinations']9 C 3[/URL] = 84
[*]Junior choices: [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=4&pl=Combinations']7 C 4[/URL] = 35
[*]Senior choices: [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=5&pl=Combinations']7 C 5 [/URL]= 21
[/LIST]
The number of committees we can choose is the product of combinations of freshmen, sophomores, juniors, and seniors.
Total Committees = Freshmen choices * Sophomore choices * Junior choices * Senior choices
Total Committees = 15 * 84 * 35 * 21
Total Committees = [B]926,100[/B]

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per square yard. How much will the chalkboard cost?
Area of a chalkboard is denoted as :
A = lw
Given 1 yard width and 2 years length of the chalkboard, we have:
A = 2(1)
A = 2 square yards
Therefore, total cost is:
Total Cost = $27.31 * square yards
Total Cost = $27.31(2)
Total Cost = [B]$54.62[/B]

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?
Take this algebraic expression in pieces:
[LIST]
[*]Let the secret number be n.
[*]Added to means we add 6 to n: n + 6
[*]The total is multiplied by 5: 5(n + 6)
[*]The phrase [I]to get[/I] means equal to, so we set 5(n + 6) equal to 50
[/LIST]
5(n + 6) = 50
To solve this equation for n, we type it in our search engine and we get:
n = [B]4[/B]

A set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal

A set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal chairs cost per chair?
[U]Wooden Chair Unit Cost:[/U]
Unit Cost = Total Cost / Quantity
Unit Cost = 444/6
Unit Cost = 74
[B][/B]
[U]Metal Chair Unit Cost:[/U]
Unit Cost = Total Cost / Quantity
Unit Cost = 720/8
Unit Cost = 90
[B][B][/B][/B]
Find the difference (how much more)
Difference = Metal Chair Unit Cost - Wooden Chair Unit Cost
Difference = 90 - 74
Difference = [B]16[/B]

A shirt costs 15 and jeans costs 25. write an expressions for the costs of j jeans and s shirts

A shirt costs 15 and jeans costs 25. write an expressions for the costs of j jeans and s shirts.
Cost equals quantity times price, so we have the total cost C:
[B]C(s, j) = 15s + 25j[/B]

A soda cost $100. What is the cost of y sodas?

A soda cost $100. What is the cost of y sodas?
Total cost = price * quantity
Total Cost = [B]100y[/B]

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every n minut

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every [I]n[/I] minutes. How many minutes until the spacecraft has no air?
800 cubic feet / .4 cubic feet every n minutes = 2000 (n minute parts)
Total time = [B]2000n[/B]

A spinner has 10 equally sized sections, 2 are gray 8 are blue. The spinner is spun twice. What is t

A spinner has 10 equally sized sections, 2 are gray 8 are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second lands on gray?
P(blue) = Blue sections / Total Sections
P(blue) = 8/10
[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get:
P(blue) = 4/5
P(gray) = Gray sections / Total Sections
P(blue) = 2/10
[URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get:
P(gray) = 1/5
We want the probability of blue,gray. Since each spin is independent, we multiply the two probabilities to get our answer:
P(blue, gray) = P(blue) * P(gray)
P(blue, gray) = 4/5 * 1/5
P(blue, gray) = [B]4/25[/B]

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 w

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 white. The pointer is spun and a marble is picked at random.
a) Use a tree diagram to list the possible outcomes.
[LIST=1]
[*][B]A, Grey[/B]
[*][B]A, Black[/B]
[*][B]A, White[/B]
[*][B]B, Grey[/B]
[*][B]B, Black[/B]
[*][B]B, White[/B]
[*][B]C, Grey[/B]
[*][B]C, Black[/B]
[*][B]C, White[/B]
[/LIST]
b) What is the probability of:
i) spinning A?
P(A) = Number of A sections on spinner / Total Sections
P(A) = [B]1/3[/B]
---------------------------------
ii) picking a grey marble?
P(A) = Number of grey marbles / Total Marbles
P(A) = [B]1/3[/B]
---------------------------------
iii) spinning A and picking a white marble?
Since they're independent events, we multiply to get:
P(A AND White) = P(A) * P(White)
P(A) was found in i) as 1/3
Find P(White):
P(White) = Number of white marbles / Total Marbles
P(White) = 1/3
[B][/B]
Therefore, we have:
P(A AND White) = 1/3 * 1/3
P(A AND White) = [B]1/9[/B]
---------------------------------
iv) spinning C and picking a pink marble?
Since they're independent events, we multiply to get:
P(C AND Pink) = P(C) * P(Pink)
Find P(C):
P(C) = Number of C sections on spinner / Total Sections
P(C) = 1/3
[B][/B]
Find P(Pink):
P(Pink) = Number of pink marbles / Total Marbles
P(Pink) = 0/3
[B][/B]
Therefore, we have:
P(C AND Pink) = 1/3 * 0
P(C AND Pink) = [B]0[/B]

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the prob

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the probability that it will land on a green section? Write your answer as a fraction or whole number.
P(green) = Total Green / Total spaces
P(green) = 2/6
We can simplify this fraction. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']type 2/6 into our search engine[/URL], choose Simplify, and we get:
P(green) = [B]1/3[/B]

A sports tournament has c teams. Each team has 17 players. Using c, write

A sports tournament has c teams. Each team has 17 players. Using c, write an expression for the total number of players in the tournament.
Total Players = Total Teams * Players Per Team
Total Players =[B] 17c[/B]

A sports tournament has d teams. Each team has 14 players. Using d, write an expression for the tota

A sports tournament has d teams. Each team has 14 players. Using d, write an expression for the total number of players in the tournament.
Tournament Players = Players per team * Number of Teams
Tournament Players = [B]14d[/B]

A store manager must calculate the total number of winter hats available to sell in the store from a

A store manager must calculate the total number of winter hats available to sell in the store from a starting number of 293. In the past month, the store sold 43 blue hats, 96 black hats, 28 red hats, and 61 pink hats. The store received a shipment of 48 blue hats, 60 black hats, 18 red hats, and 24 pink hats. How many total hats does the store have for sale?
[LIST=1]
[*]We start with 293 hats
[*]We calculate the hats sold: (43 + 96 + 28 + 61) = 228
[*]We subtract Step 2 from Step 1 to get remaining hats before the shipment: 293 - 228 = 65
[*]Now we calculate the number of hats received in the shipment: (48 + 60 + 18 + 24) = 150
[*]We add Step 4 to Step 3: 65 + 150 = [B]215 hats for sale[/B]
[/LIST]

A student and the marine biologist are together at t = 0. The student ascends more slowly than the m

A student and the marine biologist are together at t = 0. The student ascends more slowly than the marine biologist. Write an equation of a function that could represent the student's ascent. Please keep in mind the slope for the marine biologist is 12.
Slope means rise over run.
In this case, rise is the ascent distance and run is the time.
12 = 12/1, so for each second of time, the marine biologist ascends 12 units of distance
If the student ascends slower, than the total distance gets reduced by an unknown factor, let's call it c. So we have the student's ascent function as:
[B]y(t) = 12t - c[/B]

A teacher had 54 pencils gave p pencils to each of his s students. How many pencils does he have lef

A teacher had 54 pencils gave p pencils to each of his s students. How many pencils does he have left?
If the teacher gave p pencils to each of his s students, then he gave away ps total pencils.
He's left with:
[B]54 - ps[/B]

a teacher puts 1125 marbles into 9 containers to put the same number of marbles into each container

a teacher puts 1125 marbles into 9 containers to put the same number of marbles into each container how many marbles does the teacher put into each container
marbles per container = Total marbles / total containers
marbles per container = 1125/9
marbles per container = [B]125[/B]

A television sells for $750. Instead of paying the total amount at the time of the purchase, the sam

A television sells for $750. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $100 down and $50 a month for 14 months. How much is saved by paying the total amount at the time of the purchase?
Option 2:
100 + 50(14)
100 + 700
800
800 - 750 = [B]$50 saved[/B]

A test has three true-false questions. Find the total number of ways you can answer the three questi

A test has three true-false questions. Find the total number of ways you can answer the three questions
We can either choose T or F. So we have:
Question 1: 2 choies
Question 2: 2 choices
Question 3: 2 choices
2 * 2 * 2 = [B]8 choices
[/B]
[LIST=1]
[*][B]TTT[/B]
[*][B]TTF[/B]
[*][B]TFT[/B]
[*][B]FTT[/B]
[*][B]FTF[/B]
[*][B]FFT[/B]
[*][B]TFF[/B]
[*][B]FFF[/B]
[/LIST]

A test has twenty questions worth 100 points total. the test consists of true/false questions worth

A test has twenty questions worth 100 points total. the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many true/false questions are on the test?
Let m be the number of multiple choice questions and t be the number of true/false questions. We're given:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We can solve this system of equations 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the following answers:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]
Check our work in equation 1:
5 + 15 ? 20
[I]20 = 20[/I]
Check our work in equation 2:
11(5) + 3(15) ? 100
55 + 45 ? 100
[I]100 = 100[/I]

a textbook store sold a combined total of 296 sociology and history text books in a week. the number

a textbook store sold a combined total of 296 sociology and history text books in a week. the number of history textbooks sold was 42 less than the number of sociology textbooks sold. how many text books of each type were sold?
Let h = history book and s = sociology books. We have 2 equations:
(1) h = s - 42
(2) h + s = 296
Substitute (1) to (2)
s - 42 + s = 296
Combine variables
2s - 42 = 296
Add 42 to each side
2s = 338
Divide each side by 2
s = 169
So h = 169 - 42 = 127

A textbook store sold a combined total of 307 biology and chemistry textbooks in a week. The number

A textbook store sold a combined total of 307 biology and chemistry textbooks in a week. The number of chemistry textbooks sold was 71 less than the number of biology textbooks sold. How many textbooks of each type were sold?
Let b be the number of biology books and c be the number of chemistry books. We have two equations:
[LIST=1]
[*]b + c = 307
[*]c = b - 71
[/LIST]
Substitute (2) into (1) for c
b + (b - 71) = 307
Combine like terms:
2b - 71 = 307
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2b-71%3D307&pl=Solve']equation solver[/URL], we get:
[B]b = 189[/B]
Now substitute that into (2):
c = 189 - 71
[B]c = 118[/B]

A theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number x of

A theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number x of rows in the theater.
Let x be the number of rows in the theater:
x = Total Seats / Seats per row
x = 1200/20
x = [B]60[/B]

A theatre contains 459 seats and the ticket prices for a recent play were $53 for adults and $16 for

A theatre contains 459 seats and the ticket prices for a recent play were $53 for adults and $16 for children. If the total proceeds were $13,930 for a sold- out matinee, how many of each type of ticket were sold?
Let a be the number of adult tickets and c be the number of children tickets. We have the following equations:
[LIST=1]
[*]a + c =459
[*]53a + 16c = 13930
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a%2Bc%3D459&term2=53a+%2B+16c+%3D+13930&pl=Cramers+Method']simultaneous equation calculator[/URL], we have:
[B]a = 178
c = 281[/B]

A three digit number, if the digits are unique

A three digit number, if the digits are unique
[LIST=1]
[*]For our first digit, we can start with anything but 0. So we have 9 options
[*]For our second digit, we can use anything but 9 since we want to be unique. So we have 9 options
[*]For our last digit, we can use anything but the first and second digit. So we have 10 - 2 = 8 options
[/LIST]
Our total 3 digit numbers with all digits unique is found by the fundamental rule of counting:
9 * 9 * 8 = [B]648 possible 3 digit numbers[/B]

A tire repair shop charges $5 for tool cost and $2 for every minute the worker spends on the repair.

A tire repair shop charges $5 for tool cost and $2 for every minute the worker spends on the repair. A) Write an equation of the total cost of repair, $y, in terms of a total of x minutes of repair.
y = Variable Cost + Fixed Cost
y = Cost per minute of repair * minutes of repair + Tool Cost
[B]y = 2x + 5[/B]

A toffee jar contains 225 toffees . How many toffees will be there in 62 such toffee jars ?

A toffee jar contains 225 toffees . How many toffees will be there in 62 such toffee jars ?
Total Toffees = Toffee per jar * number of jars
Total Toffees = 225 * 62
Total Toffees = [B]13,950 toffees[/B]

a total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rat

a total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rate if the annual interest is $430?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4000&i1=10&i2=15&itot=430&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]3,400[/B] @ 10%
[*][B]600[/B] @ 15%
[/LIST]

A total of $4300 was invested, part of it at 6% interest and the remainder at 9%. If the total yearl

A total of $4300 was invested, part of it at 6% interest and the remainder at 9%. If the total yearly interest amounted to $315, how much was invested at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4300&i1=6+&i2=9&itot=315&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1: 2,400[/B]
[*][B]Fund 2: 1,900[/B]
[/LIST]

A total of $6,000 was invested, a portion at 6% and the remainder at 8%. The total amount of interes

A total of $6,000 was invested, a portion at 6% and the remainder at 8%. The total amount of interest earned was $450. How much was invested at each rate?
Using our split fund interest calculator, we get:
[LIST]
[*][B]1500 in 6% fund[/B]
[*][B]4500 in 8% fund[/B]
[/LIST]

A total of $7000 is invested: part at 7% and the remainder at 9%. How much is invested at each rate

A total of $7000 is invested: part at 7% and the remainder at 9%. How much is invested at each rate if the annual interest is $550?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=7000&i1=7&i2=9&itot=550&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1: $4,000[/B]
[*][B]Fund 2: $3,000[/B]
[/LIST]

a total of 6000 is invested part at 8% and the remainder at 13%. how much is invested at each rate i

a total of 6000 is invested part at 8% and the remainder at 13%. how much is invested at each rate if the annual interest is 710
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=6000&i1=8&i2=13&itot=710&pl=Calculate']split fund interest calculator[/URL], we get:
1,400
4,600

A total of 7000 is invested part at 7% and the reminder at 11% .how much is invested at each rate of

A total of 7000 is invested part at 7% and the reminder at 11% .how much is invested at each rate of the annual interest is 640
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=7000&i1=7&i2=11&itot=640&pl=Calculate']split fund interest rate calculator[/URL], we get:
[LIST]
[*]Fund 1 = [B]3250[/B]
[*]Fund 2 = [B]3750[/B]
[/LIST]

a total of one and x is less than 5

a total of one and x is less than 5
A total of one and x means we add x to 1:
1 + x
We set up an inequality, where 1 + x is less than (<) 5
[B]1 + x < 5[/B]

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continuous at a constant speed of 40 feet per minute for the last 50 feet.
(i) Determine which animal won the race.
(ii). By how much time the animal won the race.
(iii) Explain one life lesson from the race.
We know the distance formula is:
d = rt
For the turtle, he has a rate (r) of 20 feet / minute and distance (d) of 100. We want to solve for time:
[URL='https://www.mathcelebrity.com/drt.php?d=+100&r=+20&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 5
The rabbit has 3 parts of the race:
Rabbit Part 1: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Rabbit Part 2: The rabbit stops for 3 minutes (t = 3)
Rabbit Part 3: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Total time for the rabbit from the 3 parts is (t) = 1.25 + 3 + 1.25
Total time for the rabbit from the 3 parts is (t) = 5.5
[LIST]
[*](i) The [B]turtle won[/B] the race because he took more time to finish and they both started at the same time
[*](ii) We subtract the turtles time from the rabbit's time: 5.5 - 5 = [B]0.5 minutes which is also 30 seconds[/B]
[*](iii) [B]Slow and Steady wins the race[/B]
[/LIST]

A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold
Let c be the number of CDs sold, and v be the number of videos sold. We're given 2 equations:
[LIST=1]
[*]c + v = 40
[*]4c + 6v = 180
[/LIST]
You can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we choose, we get [B]c = 30, v = 10[/B].
Now let's check our work for both given equations for c = 30 and v = 10:
[LIST=1]
[*]30 + 10 = 40 <-- This checks out
[*]4c + 6v = 180 --> 4(30) + 6(10) --> 120 + 60 = 180 <-- This checks out
[/LIST]

A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold.
Let the number of cd's be c and number of videos be v. We're given two equations:
[LIST=1]
[*]c + v = 40
[*]4c + 6v = 180
[/LIST]
We can solve this system of equations using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[B]c = 30
v = 10[/B]

A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor

A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost?
Let the cost of the soda be p. So the cost of a hot dog is 2p.
The total cost of hot dogs:
2hp
The total cost of sodas:
ps
The total cost of both equals d. So we set the total cost of hots dogs plus sodas equal to d:
2hp + ps = d
We want to know the cost of a soda (p). So we have a literal equation. We factor out p from the left side:
p(2h + s) = d
Divide each side of the equation by (2h + s)
p(2h + s)/(2h + s) = d/(2h + s)
Cancel the (2h + s) on the left side, we get:
p = [B]d/(2h + s[/B])

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?
Set up a cost function C(m) where m is the number of movies you rent:
C(m) = Rental cost per movie * m + Membership Fee
[U]Video Store 1 cost function[/U]
C(m) = 1m + 7.5
Video Store 2 cost function:
C(m) = 2.50m
We want to know when the costs are the same. So we set each C(m) equal to each other:
m + 7.5 = 2.50m
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B7.5%3D2.50m&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]5[/B]

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked.
Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5.
Let Level distance = L and hill distance = H. Add the times it took for each section of the walk:
L/4 + H /3 + H/6 + L/4 = 5
The LCD of this is 12 from our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=6&pl=LCM']LCD Calculator[/URL]
[U]Multiply each side through by our LCD of 12[/U]
3L + 4H + 2H + 3L = 60
[U]Combine like terms:[/U]
6L + 6H = 60
[U]Divide each side by 3:[/U]
2L + 2H = 20
The woman walked [B]20 miles[/B]

A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the z

A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the zoo. How many penguins live at the zoo?
Let p be the total number penguins at the zoo.
We're told:
30% of p = 15
Since 30% = 0.3, we have:
0.3p = 15
Solve for [I]p[/I] in the equation 0.3p = 15
[SIZE=5][B]Step 1: Divide each side of the equation by 0.3[/B][/SIZE]
0.3p/0.3 = 15/0.3
p = [B]50[/B]

Aaron bought a guitar for n dollars. The tax in his state is 6%. What is the total cost of the guita

Aaron bought a guitar for n dollars. The tax in his state is 6%. What is the total cost of the guitar including tax?
Sale price is n
Tax on sale is 0.06n
Add them together
n + 0.06n = [B]1.06n[/B]

Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar

Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar cookies and 6 oatmeal raisin cookies. What it’s the probability that Aaron randomly selects a peanut butter cookie from the bag, eats it,, then randomly selects another peanut butter cookie?
First draw out of the bag is a peanut butter cookie:
P(PB) = Total Peanut Butter Cookies / Total Cookies
P(PB) = 6/27
Second draw out of the bag is a peanut butter cookie, but we have one less since Aaron ate one:
P(PB) = Total Peanut Butter Cookies - 1 / Total Cookies - 1
P(PB) = (6 - 1)/(27 - 1)
P(PB) = 5/26
Now, since each event is independent, we multiply them to see the probability of choosing a peanut butter cookie, eating it, then reaching in and choosing another peanut butter cookie:
P(PB, PB) = 6/27 * 5/26
[URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F27&frac2=5%2F26&pl=Multiply']P(PB, PB)[/URL] = [B]5/117[/B]

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applie

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying [I]x[/I] nights?
[LIST]
[*]The Room cost equals 99.95 times x where x is the number of rooms
[*]We express an 8% tax by multiplying the room cost by 1.08
[*]Finally, we add on $5, which is [I]untaxed[/I]
[/LIST]
[I][/I]
Take this in pieces:
Room Cost: 99.95x
Tax on Room 1.08(99.95x)
Add on $5 which is untaxed: [B]1.08(99.95x) + 5[/B]

Adam drove the 10 miles to school at a speed of 60 mph. On his way home, due to traffic, his speed w

Adam drove the 10 miles to school at a speed of 60 mph. On his way home, due to traffic, his speed was 30 mph. What was his average speed for the round trip to school and back?
D = rt
To school:
60 miles in 60 minutes = 10 miles in 10 minutes
To home:
30 miles in 60 minutes = 10 miles in 20 minutes
Total time:
10 + 20 = 30 minutes or 0.5 hours
With a speed of s, we have:
d = st
20 = 0.5s
Divide each side by 2:
s = [B]40 mph[/B]

Adam has 20 sweets he eats a quarter of them how many does he have left?

Adam has 20 sweets he eats a quarter of them how many does he have left?
A quarter means 1/4. There's 2 ways you can approach this problem.
[B][U]Approach #1:[/U][/B]
Adam eats a quarter, or 1/4 of the sweets. So he eats:
20 * 1/4 = 5
Remaining sweets = Total Apples - Eaten Apples
Remaining sweets = 0 - 5
Remaining sweets= 15
[U][B]Approach #2:[/B][/U]
If Adam eats 1/4 of the sweets, this means he has:
1 - 1/4 sweets remaining.
Since 1 equals 4/4, we have:
4/4 - 1/4 = 3/4
Therefore, he has 20 * 3/4 sweets remaining.
This is 60/4, or [B]15[/B]

add x and 3; then multiply by y

Add x and 3
x + 3
Then multiply by y (they mean the total)
[B]y(x + 3)[/B]

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were col

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair
Let the number of students be s and the others be o. We're given two equations:
[LIST=1]
[*]o + s = 2848
[*]3.75o + 2.50s = 10078.75
[/LIST]
Since we have no coefficients for equation 1, let's solve this the fast way using substitution. Rearrange equation 1 by subtracting o from each side to isolate s
[LIST=1]
[*]o = 2848 - s
[*]3.75o + 2.50s = 10078.75
[/LIST]
Now substitute equation 1 into equation 2:
3.75(2848 - s) + 2.50s =10078.75
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3.75%282848-s%29%2B2.50s%3D10078.75&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]481[/B]

After paying 7 dollars for the pie, Keith has 64 dollars left. How much money did he have before buy

After paying 7 dollars for the pie, Keith has 64 dollars left. How much money did he have before buying the pie?
we add the 7 dollars back in to find Keith's original total t:
t = 64 + 7
t = [B]$71[/B]

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total v

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total value of $3.50. How many of each type of coin does Ahmad have?
Let the number of 5-cent coins be f.
Let the number of 20-cent coins be t.
We're given two equations:
[LIST=1]
[*]f + t = 31
[*]0.05f + 0.2t = 3.50
[/LIST]
We can solve this simultaneous system of equations 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]f = 18[/B]
[*][B]t = 13[/B]
[/LIST]

Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per

Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per hour plus $15 extra for a wetsuit. Find the number of hours for which the total charges for both companies would be the same.
Al's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit:
C(h) = 25h
Wendy's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit:
C(h) = 20h + 15
We want to set both cost equation equal to each other, and solve for h:
20h + 15 = 25h
[URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B15%3D25h&pl=Solve']Typing this equation into our search engine[/URL], we get:
h = [B]3[/B]

Ali buys 6 sunglasses which cost $1.84 each, calculate the total cost.

Ali buys 6 sunglasses which cost $1.84 each, calculate the total cost.
Total Cost = Quantity * Price
Total Cost = 6 * $1.84
Total Cost = [B]$11.04[/B]

Ali needs to make a total of 90 deliveries this week. So far he has completed 72 of them. What perce

Ali needs to make a total of 90 deliveries this week. So far he has completed 72 of them. What percentage of his total deliveries has Ali completed
[URL='https://www.mathcelebrity.com/perc.php?num=72&den=90&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']Enter 72/90 into our search engine and choose the percentage option[/URL] and we get [B]80%[/B].

Ali spent $60 at the grocery store. Of this amount, he spent $51 on fruit. What percentage of the to

Ali spent $60 at the grocery store. Of this amount, he spent $51 on fruit. What percentage of the total did he spend on fruit?
51/60 = 0.85
Multiply 0.85 by 100 to get the percentage
0.85 * 100 = [B]85%[/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]

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike. If she rode her bike for 45 minutes in a week, how much time did she devote to homework in the same week
If Amanda spent 2/5 of her time after school doing homework, she has 1 - 2/5 time left over.
We convert 1 to a fraction using a denominator of 5, we get:
5/5 - 2/5 = 3/5
And Amanda spent 1/4 of 3/5 of her time bike riding, which means she spent:
1(3)/4(5) = 3/20 of her time.
If the total time after school is t, we have:
3t/20 = 45
[URL='https://www.mathcelebrity.com/prop.php?num1=3t&num2=45&den1=20&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing in 3t/20 = 45 to our search engine[/URL], we get t = 300.
So Amanda has 300 total minutes after school, which means she spent 2/5(300) = [B]120 minutes (2 hours)[/B] doing homework.

Amount you spend if you buy a shirt for $20 and jeans for j dollars

Amount you spend if you buy a shirt for $20 and jeans for j dollars
We want an algebraic expression for our total spend. We add the $20 for a shirt plus j for the jeans:
[B]20 + j[/B]

Amy has n decks of cards. Each deck has 52 cards in it. Using n, write an expression for the total

Amy has n decks of cards. Each deck has 52 cards in it. Using n, write an expression for the total number of cards Amy has.
[B]52n[/B]

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplan

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplane is
If we assume the sample space is either men, women, or children to get 100% of the passengers, we have:
PercentWomen = 100% - Men - Children
PercentWomen = 100% - 45% - 20%
PercentWomen = 35%
Calculate Women passengers
Women passengers = Total passengers * Percent Women
Women passengers = 500 * 35%
Women passengers = [B]175[/B]

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds,

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds, what is the maximum number of people (p) that can be on the elevator at one time?
Total weight = average weight per person * Number of people
Total weight = 150p
We know from the problem that:
150p < 2700
We want to solve this inequality for p. Divide each side of the inequality by 150:
150p/150 < 2700/150
Cancel the 150's on the left side and we get:
p < [B]18[/B]

An elevator can safely lift at most 4400 1bs. A concrete block has an average weight of 41 lbs. What

An elevator can safely lift at most 4400 1bs. A concrete block has an average weight of 41 lbs. What is the maximum number of concrete blocks that the elevator can lift?
Total blocks liftable = Lift Max / Weight per block
Total blocks liftable = 4400 / 41
Total blocks liftable = 107.31
We round down to whole blocks and we get [B]107[/B]

An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hours ove

An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hours over 35. One weeks paycheck (before deductions) was for $308.00. How many hours did the employee work?
Let's first check to see if the employee worked overtime:
Regular Hours: 35 * 7 = 245
Since the employee made $308, they worked overtime. Let's determine how much overtime money was made:
308 - 245 = 63
Now, to calculate the overtime hours, we divide overtime pay by overtime rate
63/10.50 = 6
Now figure out the total hours worked in the week:
Total Hours = Regular Pay Hours + Overtime Hours
Total Hours = 35 + 6
[B]Total Hours = 41[/B]

An estate has 6 houses and each house has x lighting fittings which need 1 lamp each, and y fittings

An estate has 6 houses and each house has x lighting fittings which need 1 lamp each, and y fittings which need 3 lamps each. Write a formula to find z, the total number of lamps needed on the estate.
z = 6(x * 1 + 3 * y)
z = [B]6(x + 3y)[/B]

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6400 dollars. I

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6400 dollars. If she earns a total of 87400 dollars per year, what is her monthly salary in dollars?
Calculate the annual salary without bonus:
Annual Salary = Total Pay - Christmas Bonus
Annual Salary = 87400 - 6400
Annual Salary = 81000
Now calculate the monthly salary. [I]Note: there are 12 months in a year[/I]:
Monthly Salary = Annual Salary / 12
Monthly Salary = 81000/12
[URL='https://www.mathcelebrity.com/fraction.php?frac1=81000%2F12&frac2=3%2F8&pl=Simplify']Monthly Salary[/URL] = [B]6750[/B]

An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function

An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function that represents the total amount he charges for designing a certain number of rooms. What is the value of the function for an input of 6, and what does it represent?
[U]Set up the cost function C(r) where r is the number of room to design:[/U]
C(r) = Cost per room * r + Site Visit Fee
C(r) = 55r + 100
[U]Now, the problem asks for an input of 6, which is [I]the number of rooms[/I]. So we want C(6) which is the [I]cost to design 6 rooms[/I]:[/U]
C(6) = 55(6) + 100
C(6) = 330 + 100
C(6) = [B]430[/B]

An international long distance phone call costs $0.79 per minute. How much will a 22 minute call cos

An international long distance phone call costs $0.79 per minute. How much will a 22 minute call cost?
[U]Calculate total cost:[/U]
Total cost = Cost per minute * number of minutes
Total cost = $0.79 * 22
Total cost = [B]$17.38[/B]

An investor invests $1000. Part of the investment is made at 5% interest and part of the investment

An investor invests $1000. Part of the investment is made at 5% interest and part of the investment is made at 10% interest. How much should be invested at 5% so the total interest in the first year is $80?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=1000&i1=5&i2=10&itot=80&pl=Calculate']split fund interest calculator[/URL], we get:
[B]$400[/B]

An organic juice bottler ideally produces 215,000 bottle per day. But this total can vary by as much

An organic juice bottler ideally produces 215,000 bottle per day. But this total can vary by as much as 7,500 bottles. What is the maximum and minimum expected production at the bottling company?
Our production amount p is found by adding and subtracting our variance amount:
215,000 - 7,500 <= p <= 215,000 + 7,500
[B](min) 207,500 <= p <=222,500 (max)[/B]

Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of

Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of milk last him?
Milk Days = Total Pints of Milk / pints drank per day
Milk Days = 8 / 1/4
Dividing by a fraction is the same as multiplying by it's reciprocal.
The [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=3%2F8&pl=Reciprocal']reciprocal of[/URL] 1/4 is 4/1, so we have:
8 * 4/1 = [B]32 days[/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]

Ann purchased 8 packs of grape gum, 12 packs of cherry gum, and 6 packs of strawberry gum. If there

Ann purchased 8 packs of grape gum, 12 packs of cherry gum, and 6 packs of strawberry gum. If there are 6 pieces in each pack, how many pieces of gum did Ann purchased?
Total Pieces = Packs x pieces per pack
Total Pieces = (8 + 12 + 6) x 6
Total Pieces = 26 x 6
Total Pieces = [B]156[/B]

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a t

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5 Ann paid a total of $49.10.
Set up the cost function C(m) where m is the number of miles:
C(m) = Mileage Rate x m + Tip
2.10m + 5 = 49.10
[URL='https://www.mathcelebrity.com/1unk.php?num=2.10m%2B5%3D49.10&pl=Solve']Type 2.10m + 5 = 49.10 into the search engine[/URL], and we get [B]m = 21[/B].

Anna is collecting boxes of cereal to deliver in a food bank. The volume of each cereal box is 324 c

Anna is collecting boxes of cereal to deliver in a food bank. The volume of each cereal box is 324 cubic inches. The picture shows the cereal boxes she has collected so far. A large delivery box holds three times as many boxes as Anna collected.
About what is the volume of the delivery box?
The picture has 12 cereal boxes. Since the delivery box holds three times as many cereal boxes as Anna collected, the delivery box holds 12 * 3 = 36 cereal boxes.
With each cereal box having a volume of 324 cubic inches, we have the total volume as:
V = 324 cubic inches * 36 cereal boxes
V = [B]11,664 cubic inches[/B]

Anthony has 8 cookies. He gives one to his friend. How many does he have left?

Anthony has 8 cookies. He gives one to his friend. How many does he have left?
When Anthony gives one cookie away, he reduces his total:
8 - 1 = [B]7 cookies left[/B]

Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop

Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?
Total shots = Shots made + shots missed
Total shots = 1 + 2
Total shots = [B]3[/B]

Aryion has 3 sets of hair ties. Each set contains 2 hair ties. How many hair ties does Aryion have?

Aryion has 3 sets of hair ties. Each set contains 2 hair ties. How many hair ties does Aryion have?
Total hair ties = Sets of hair ties * number of hair ties per set
Total hair ties = 3 * 2
Total hair ties = [B]6[/B]

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum am

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum amount of sales you need to make in order to receive a total income of at least $1500 per month.
Let the amount of sales be s. The phrase [I]at least[/I] means greater than or equal to. Since 20% is 0.2, We want to know when:
0.20s + 600 >= 1500
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.20s%2B600%3E%3D1500&pl=Solve']type this inequality into our search engine to solve for s[/URL] and we get:
s >= [B]4500[/B]

As a salesperson, Laura earns a base salary of $72 per week plus a commission of 20% of sales. If sh

As a salesperson, Laura earns a base salary of $72 per week plus a commission of 20% of sales. If she had $75 in sales last week, what was her total pay?
Total Pay = Base Pay + Commission
Calculate Commission:
Commission = Commission Percent x Sales
Commission = 20% * 75
Commission = 15
Total Pay = Base Pay + Commission
Total Pay = 72 + 15
Total Pay = [B]$97[/B]

As a salesperson, Lauren earns a base salary of $94 per week plus a commission of 10% of sales. If s

As a salesperson, Lauren earns a base salary of $94 per week plus a commission of 10% of sales. If she had $90 in sales last week, what was her total pay?
[B][U]Use the Base plus Commission formula above[/U][/B]
Salary = Base Salary + 10%(Total Sales)
Salary = $94 + 0.1(90)
Salary = $94 + $9
Salary = [B]$103[/B]

Assume that in your Abnormal Psychology class you have earned test scores of 74%, 78%, and 63%, and

Assume that in your Abnormal Psychology class you have earned test scores of 74%, 78%, and 63%, and only one test remains. If you need a mean score of 80% to earn a B for you final grade, is it possible for you to accomplish this? Assume there is no extra credit. Show work and explain why or why not. Hint: you're taking 4 tests total.
Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=74%2C78%2C63&avg=80&pl=Calculate+Missing+Score']missing average calculator with our 3 given scores and target average[/URL], we get:
A 4th score needed of 105.
Since the most you can score on an exam is 100, [B][I]this is impossible[/I][/B].

assume your math class has 10 sophomores and 7 juniors. there are 3 female sophomores and 4 male jun

assume your math class has 10 sophomores and 7 juniors. there are 3 female sophomores and 4 male juniors. what is the probability of randomly selecting a student who is a female or a junior
[U]Sophomores:[/U]
10 sophomores:
3 female
male = 10 - 3 = 7
[U]Juniors:[/U]
7 juniors
4 males
female = 7 - 4 = 3
[U]Females:[/U]
Total Females = Female Sophomores + Female Juniors
Total Females = 3 + 3
Total Females = 6
[U]Total Students:[/U]
Total Students = Total Sophomores + Total Juniors
Total Students = 10 + 7
Total Students = 17
[U]We want P(female or Junior). We use the formula below to avoid duplicates:[/U]
P(female or Junior) = P(female) + P(junior) - P(female and junior)
P(female or Junior) = Total Females / Total Students + Total Juniors / Total Students - Total Female Juniors / Total Students
P(female or Junior) = 6/17 + 7/17 - 3/17
P(female or Junior) = [B]10/17[/B]

at 9:30am you enter a parking garage. It cost $3.25 for each hour to park your car. You leave the ga

at 9:30am you enter a parking garage. It cost $3.25 for each hour to park your car. You leave the garage at 2:00pm. How much does it cost to park?
[U]Calculate Hours:[/U]
9:30 am to 10:00 am is 0.5 hours
10 am to 2 pm is 4 hours
So our total time is 4.5 hours
[U]Calculate Total Cost[/U]
Total Cost = Hours * Cost per hour
Total Cost = 4.5 * 3.25
Total Cost = [B]$14.63[/B]

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slic

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slices of pie costs $20.20. what is the cost of one cupcake?
Let the number of cupcakes be c
Let the number of pie slices be p
Total Cost = Unit cost * quantity
So we're given two equations:
[LIST=1]
[*]1c + 2p = 12.40
[*]2c + 3p = 20.20
[/LIST]
We can solve this system of equations any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]c = 3.2[/B]
[*]p = 4.6
[/LIST]

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 m

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold?
Let the number of adult tickets be a. Let the number of child tickets be c. We're given two equations:
[LIST=1]
[*]c = a + 30
[*]6a + 4c = 6360
[/LIST]
Substitute equation (1) into equation (2):
6a + 4(a + 30) = 6360
Multiply through to remove parentheses:
6a + 4a + 120 = 6360
T[URL='https://www.mathcelebrity.com/1unk.php?num=6a%2B4a%2B120%3D6360&pl=Solve']ype this equation into our search engine[/URL] to solve for a and we get:
a = 624
Now substitute a = 624 back into equation (1) to solve for c:
c = 124 + 30
c = [B]154[/B]

At a concert there were 25 more women than men. The total number of people at the concert was 139. F

At a concert there were 25 more women than men. The total number of people at the concert was 139. Find the number of women and the number of men at the concert.
Let men be m and women be w. We're given two equations.
[LIST=1]
[*]w = m + 25
[*]m + w = 139
[/LIST]
Substitute equation (1) into equation (2):
m + m + 25 = 139
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2B25%3D139&pl=Solve']type this equation into our search engine[/URL] and we get:
m = [B]57
[/B]
To find w, we substitute m = 57 into equation (1):
w = 57 + 25
w = [B]82[/B]

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert was 360, what was the total number of audience members?
We're looking for total audience members where [I]20% of what equals 360[/I]?
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=360&pct1=20&pcheck=2&pct2=+70&den1=+80&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Type this expression into our search engine[/URL] and we get:
Audience = [B]1,800[/B]

At a festival, Cherly bought 5 ride tokens and 9 game tokens. She spent $59. Let x represent the cos

At a festival, Cherly bought 5 ride tokens and 9 game tokens. She spent $59. Let x represent the cost of ride tokens and let y represent the cost of game tokens. Write an equation in standard for that can be used to determine how much each type of token costs.
We know that:
Token Cost + Game Cost = Total Cost
Since cost = price * quantity, we have:
[B]5x + 9y = 59[/B]

At a football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs

At a football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs sold was 59 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
[U]Let h = number of hot dogs and s = number of sodas. Set up our given equations:[/U]
[LIST=1]
[*]h + s = 117
[*]h = s - 59
[/LIST]
[U]Substitute (2) into (1)[/U]
(s - 59) + s = 117
[U]Combine s terms[/U]
2s - 59 = 117
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2s-59%3D117&pl=Solve']equation solver[/URL], we find:[/U]
[B]s = 88
[/B]
[U]Plug s = 88 into (2)[/U]
h = 88 - 59
[B]h = 29[/B]

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers fo

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.5. How many slices of pizza did they sell
Let the number of pizza slices be p and the number of hamburgers be h. We're given two equations:
[LIST=1]
[*]p = h + 40
[*]1.35h + 0.75p = 292.50
[/LIST]
[I]Substitute[/I] equation (1) into equation (2) for p:
1.35h + 0.75(h + 40) = 292.50
1.35h + 0.75h + 30 = 292.50
2.10h + 30 = 292.50
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.10h%2B30%3D292.50&pl=Solve']plug this equation into our search engine[/URL] and we get:
h = 125
The problem asks for number of pizza slices sold (p). So we substitute our value above of h = 125 into equation (1):
p = 125 + 40
p = [B]165[/B]

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2.
[LIST]
[*]How many men at the party?
[*]How many ladies at the party?
[*]How many kids at the party?
[/LIST]
Our total ratio denominator is 4 + 3 + 2 = 9. To find the number of each type of person, we take their ratio divided by their ratio numerator times 72 people at the party
[U]Calculate ratios:[/U]
[LIST]
[*]Men: [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F9&frac2=72&pl=Multiply']4/9 * 72[/URL] = [B]32[/B]
[*]Ladies: [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=72&pl=Multiply']3/9 * 72[/URL] = [B]24[/B]
[*]Kids: [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F9&frac2=72&pl=Multiply']2/9 * 72[/URL] = [B]16[/B]
[/LIST]
[U]Check our work:[/U]
Men + Ladies + Kids = 32 + 24 + 16
Men + Ladies + Kids = 72 <-- This checks out!

At a rate of 4 gallons per min , how long will it take to fill a 300 gallon swimming pool

At a rate of 4 gallons per min , how long will it take to fill a 300 gallon swimming pool
Time to fill = Total Gallons of the Pool / Fill Rate
Time to Fill = 300 gallons / 4 gallons per minute
Time to Fill = [B]75 minutes[/B]

At Costco, a case of 12 boxes of macaroni and cheese costs $18.00. How much is each box of macaroni

At Costco, a case of 12 boxes of macaroni and cheese costs $18.00. How much is each box of macaroni and cheese worth?
Cost per box = Total price / number of boxes
Cost per box = $18/12
Cost per box = [B]$1.50[/B]

At Falling Creek Middle School, they noticed that 3 out of every 4 buses were on time. If there are

At Falling Creek Middle School, they noticed that 3 out of every 4 buses were on time. If there are a total of 32 buses that drop off at this school, how many buses will NOT be on time.
If 3/4 are on time, we have 1 - 3/4 are not on time.
1 = 4/4
4/4 - 3/4 = 1/4 are not on time
We multiply 1/4(32) = [B]8 buses will NOT be on time[/B].

At Sams Club, 32 cans of Coke cost a total of $8.96. What is the cost per can?

At Sams Club, 32 cans of Coke cost a total of $8.96. What is the cost per can?
Unit Cost is Total Cost / Number of Units
Unit Cost = $8.96/32
Unit Cost = [B]$0.28[/B]

At the 2002 Winter Olympics, Austria won 2 gold medals. This was 1/8 of the total medals Austria won

At the 2002 Winter Olympics, Austria won 2 gold medals. This was 1/8 of the total medals Austria won. How many did Austria win?
Let t be the total medals Austria won. We have:
2 = x/8
Cross multiply, we get:
x = 2 * 8
x = [B]16[/B]

At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the N

At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the NY Knicks played a total of 72 times. Find a solution to this problem and explain.
Let w be the number of wins
Let l be the number of losses
We're given two equations:
[LIST=1]
[*]w = l + 10
[*]l + w = 72
[/LIST]
To solve this system of equations, substitute equation (1) into equation (2) for w:
l + l + 10 = 72
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2Bl%2B10%3D72&pl=Solve']type it in our math engine[/URL] and we get:
l = [B]31
[/B]
To solve for w, we substitute l = 31 into equation (1):
w = 31 + 10
w = [B]41[/B]

At Zabowood’s Gadget Store, some items are paid on instalment basis through credit cards. Clariza wa

[B]A[/B]t Zabowood’s Gadget Store, some items are paid on instalment basis through credit cards. Clariza was able to sell 10 cellphones costing Php 18,000.00 each. Each transaction is payable in 6 months equally divided into 6 equal instalments without interest. Clariza gets 2% commission on the first month for each of the 10 cellphones. Commission decreases by 0.30% every month thereafter and computed on the outstanding balance for the month. How much commission does Clariza receive on the third month?
Calculate Total Sales Amount:
Calculate Total Sales Amount = 10 cellphones * 18000 per cellphone
Calculate Total Sales Amount = 180000
Calculate monthly sales amount installment:
monthly sales amount installment = Total Sales Amount / 6
monthly sales amount installment = 180000/6
monthly sales amount installment = 30000 per month
Calculate Third Month Commission:
Third month commission = First Month Commission - 0.30% - 0.30%
Third month Commission = 2% - 0.30% - 0.30% = 1.4%
Calculate 3rd month commission amount:
3rd month Commission amount = 1.4% * 30000
3rd month Commission amount = [B]420[/B]

b bags of beans there are 7 beans in each bag

b bags of beans there are 7 beans in each bag
This means we have 7 beans x b bags = 7b beans total beans.

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, ab

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years.
At any time t, the Bangladesh population at year t is:
[B]y = 170,000,000(1.015)^t[/B]

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants co

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use.
[U]Define variables[/U]
[LIST]
[*]Let c be the number of corn plants
[*]Let p be the number of potato plants
[/LIST]
Since cost = price * quantity, we're given two inequalities:
[LIST=1]
[*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B]
[*][B]c + p < 15[/B]
[/LIST]

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each p

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each pencil
The cost per pencil is:
1560/30 = 52
Build revenue function:
Revenue = Number of Pencils * Sales Price (s)
Revenue = 30s
The profit equation is:
Profit = Revenue - Cost
Given profit is 180 and cost is 1560, we have:
30s - 1560 = 180
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=30s-1560%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 58
This is sales for total profit. The question asks profit per pencil.
Profit per pencil = Revenue per pencil - Cost per pencil
Profit per pencil = 58 - 52
Profit per pencil = [B]6[/B]

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money in terms of the number of quarters and dimes. b)Rearrange the equation to isolate for the number of dimes (D)
a) The equation is:
[B]0.1d + 0.25q = 4.5[/B]
b) Isolate the equation for d. We subtract 0.25q from each side of the equation:
0.1d + 0.25q - 0.25q = 4.5 - 0.25q
Cancel the 0.25q on the left side, and we get:
0.1d = 4.5 - 0.25q
Divide each side of the equation by 0.1 to isolate d:
0.1d/0.1 = (4.5 - 0.25q)/0.1
d = [B]45 - 2.5q[/B]

Benny bought a soft drink for 2 dollars and 7 candy bars. He spent a total of 27 dollars. How much d

Benny bought a soft drink for 2 dollars and 7 candy bars. He spent a total of 27 dollars. How much did each candy bar cost?
[U]Calculate the candy bar spend:[/U]
Candy Bar Spend = Total Spend - Soft Drink
Candy Bar Spend = 27 - 2
Candy Bar Spend = 25
[U]Calculate the cost of each candy bar:[/U]
Cost of each candy bar = Candy Bar Spend / Total Candy Bars
Cost of each candy bar = 25 / 7
Cost of each candy bar = [B]3.57[/B]

Benny opened a bank account. He deposited $92.50 into his account every month for 10 months. He used

Benny opened a bank account. He deposited $92.50 into his account every month for 10 months. He used $36.50 every month to pay for art lessons. After 10 months, he used 1/2 of the total money left in his account to go to a summer camp for artists. What is the total amount of money Benny spent to go to the summer camp?
If Benny deposits $92.50 every month and withdraws $36.50 every month, his net deposit each month is:
92.50 - 36.50 = 56
Benny does this for 10 months, so his balance after 10 months is:
56 * 10 = 560
Half of this is:
560/2 = [B]280[/B]

Bill raises the flag 15 feet above the ground. Then he lowers it 8 feet and raises it another 2 feet

Bill raises the flag 15 feet above the ground. Then he lowers it 8 feet and raises it another 2 feet. how far above the ground is the flag now?
We tally up the positives and negatives:
Raise = +15
Lower = -8
Raise = +2
Total = +15 - 8 + 2
Total = [B]9 feet above the ground[/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]

Blanca works as a salesperson and earns a base salary of $72 per week plus a commission of 12% of al

Blanca works as a salesperson and earns a base salary of $72 per week plus a commission of 12% of all her sales. If Blanca had $75 in weekly sales, how much did she make?
[U]Find the commission on her sales[/U]
Commission = Sales * 12%
Commission = 75 * 0.12 = 9
[U]Now add in her base salary[/U]
Total Salary = Base Salary + Commission
Total Salary = 72 + 9
Total Salary = [B]81[/B]

Bob has 4/5 of a pound of fudge. He wants to share it with Sue. How much of a pound of fudge will bo

Bob has 4/5 of a pound of fudge. He wants to share it with Sue. How much of a pound of fudge will both of them get?
If Bob shares the fudge with Sue, we assume they split equal parts. This means:
We take 4/5 total and divide into 2 for 2 people:
4/5/2
This is the same as 4/5 * 1/2
4/10
This fraction is not simplified.
Factor of 4 = {1, [U]2[/U], 4}
Factors of 10 = {1, [U]2[/U], 5, 10}
In both of these lists, we see the greatest common factor is 2.
So we divide top and bottom of 4/10 by 2:
4/2 / 10 / 2
[B]2/5
Bob gets 2/5 of a pound of fudge and Sue gets [B]2/5 of a pound of fudge[/B][/B]

Bob has a bookcase with 4 shelves. There are k books on each shelf. Using k, write an expression for

Bob has a bookcase with 4 shelves. There are k books on each shelf. Using k, write an expression for the total number of books.
Total Books = Bookcases * shelves per bookcase * books per shelf
Total Books = 1 * 4 * k
Total Books = [B]4k[/B]

Bob ordered a burger and fries for $8.99. He also got a coke for $1.50. What is his subtotal?

Bob ordered a burger and fries for $8.99. He also got a coke for $1.50. What is his subtotal?
Subtotal = Burger and fries + Coke
Subtotal = 8.99 + 1.50
Subtotal = [B]10.49[/B]

Brenda has already knit 4 centimeters of scarf, and can knit 1 centimeter each night. After 43 night

Brenda has already knit 4 centimeters of scarf, and can knit 1 centimeter each night. After 43 nights of knitting, how many centimeters of scarf will Brenda have knit in total?
1 centimeter per night * 43 nights = 43 centimeters knitted.
Add that to the 4 centimeters she started with, and we have:
43 + 4 = [B]47 centimeters[/B]

Brendan bought an aquarium originally priced at $50 but on sale for 50% off. After 12% sales tax, wh

Brendan bought an aquarium originally priced at $50 but on sale for 50% off. After 12% sales tax, what was the total cost?
50% off of 50 means they pay half, or 1/2(50) = 25.
Now, this gets taxed at 12%. So we multiply 25 * 1.12
Total Cost = 25(1.12)
Total Cost = [B]$28[/B]

Brice has 1200 in the bank. He wants to save a total of 3000 by depositing 40 per week from his payc

Brice has 1200 in the bank. He wants to save a total of 3000 by depositing 40 per week from his paycheck. How many weeks will it take until he saves 3000?
Remaining Savings = 3,000 - 1,200 = 1,800
40 per week * x weeks = 1,800
40x = 1800
Divide each side of the equation by 40
[B]x = 45 weeks[/B]

Bridget can grow 6 flowers with every seed packet. With 4 seed packets, how many total flowers can B

Bridget can grow 6 flowers with every seed packet. With 4 seed packets, how many total flowers can Bridget have in her garden?
Set up a proportion of flowers to seed packets where f is the number of flowers for 4 seed packets. We have:
6/1 = f/4
Cross multiply:
f(1) = 24
f = 24

Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per

Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per month
Let Bud's earnings be b.
Let Maxine's earnings be m.
We're given two equations:
[LIST=1]
[*]b = m + 400
[*]b + m = 3600
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for b
m + 400 + m = 3600
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B400%2Bm%3D3600&pl=Solve']type it in our search engine[/URL] and we get:
m = 1600
To solve for b, we substitute m = 1600 into equation (1) above:
b = 1600 + 400
b = [B]2200[/B]

Calculate the simple interest if the principal is 1500 at a rate of 7% for 3 years

Calculate the simple interest if the principal is 1500 at a rate of 7% for 3 years.
Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=1500&int=7&t=3&pl=Simple+Interest']simple interest calculator[/URL], the total interest earned over 3 years is [B]$315[/B].

Caleb earns points on his credit card that he can use towards future purchases.

Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights, two points per dollar spent on hotels, and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 money than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.

camille has 7 blouses,2 skirts,3 pair of short pants and 5 pair of jeans.how many different outfits

camille has 7 blouses,2 skirts,3 pair of short pants and 5 pair of jeans.how many different outfits can he wear,assuming that he always wear a belt.
Using the fundamental rule of counting, we find total amount of different outfits as follows:
7 blouses * 2 skirts * 3 pair of short pants * 5 pair of jeans = [B]210 outfits[/B].

Can you solve this word problem? The Wildgrove Middle School cafeteria goes through a lot of peanut

Can you solve this word problem? The Wildgrove Middle School cafeteria goes through a lot of peanut butter. Currently, they have 120 ounces of regular peanut butter in stock. They also have 319 ounces of crunchy peanut butter. How many ounces do they have in total?
[U]Calculate Total Peanut Butter Ounces[/U]
Total Peanut Butter Ounces = Regular Peanut Butter Ounces + Crunch Peanut Butter Ounces
Total Peanut Butter Ounces = 120 + 319
Total Peanut Butter Ounces = [B]439 ounces[/B]

Cara learns to perform 2 vocal pieces during each week of lessons. After 7 weeks of voice lessons, h

Cara learns to perform 2 vocal pieces during each week of lessons. After 7 weeks of voice lessons, how many pieces will Cara be able to sing, in total?
2 vocal pieces per week x 7 weeks = 14 pieces.

Carl is taking a math test. There are 10 questions which take 30 seconds each; 15 questions which ta

Carl is taking a math test. There are 10 questions which take 30 seconds each; 15 questions which take 40 seconds each; and 12 questions which take 2 minutes each. Carl pauses for 5 seconds between questions. In addition, he sharpens his pencil twice, which takes 20 seconds each time. The test begins promptly at 10:00 am. When Carl hands in his completed test, what time is it?
[U]10 Questions:[/U]
[LIST]
[*]30 seconds each x 10 questions = 5 minutes
[*]10 pauses between questions x 5 seconds per question = 50 seconds
[/LIST]
[U]15 Questions[/U]
[LIST]
[*]40 seconds each x 15 questions = 600 seconds, or 10 minutes
[*]15 pauses between questions x 5 seconds per question = 75 seconds, or 1 minute, 15 seconds
[/LIST]
[U]12 Questions[/U]
[LIST]
[*]2 minutes x 12 questions = 24 minutes
[*]12 pauses x 5 seconds per question = 60 seconds, or 1 minute
[/LIST]
[U]2 Pencil Sharpenings[/U]
[LIST]
[*]2 pencil sharpening x 20 seconds each = 40 seconds
[/LIST]
[U]Total Time[/U]
5 minutes, 50 seconds
11 minutes, 15 seconds
25 minutes
40 seconds
41 minutes and 105 seconds
But 105 seconds is 1 minute, 45 seconds.
So we have 41 minutes, 45 seconds
Therefore, it's [B]10:41[/B]

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly hav

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly have in her backyard? Solve using unit rates.
Set up a proportion of plants per seed packets where p is the number of plants per 37 seed packets.
50/25 = p/37
Copying and pasting this problem [URL='http://www.mathcelebrity.com/prop.php?num1=50&num2=p&den1=25&den2=37&propsign=%3D&pl=Calculate+missing+proportion+value']into our search engine[/URL], we get [B]p = 74[/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]

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum d

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax
Let the original price be p.
p
Apply 25% discount first, which is the same as subtracting 0.25:
p(1 - 0.25)
Subtract 30 for in store buck
p(1 - 0.25) - 30
The phrase [I]no more than[/I] means an inequality using less than or equal to:
p(1 - 0.25) - 30 <= 60
To solve this inequality for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=p%281-0.25%29-30%3C%3D60&pl=Solve']type it in our math engine[/URL] and we get:
[B]p <= 120[/B]

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of f

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Carmen wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this.
We have:
25f + 100c < 50
Note: We use < and not <= because it states less than in the problem.

Carol bought a pair of jeans for $12.95 and a belt for $3.79. The sales tax is $1.01. Carol gave the

Carol bought a pair of jeans for $12.95 and a belt for $3.79. The sales tax is $1.01. Carol gave the store clerk a $20.00 bill. How much change should she get back?
Calculate total cost:
Total cost = Jeans + Belt + Sales Tax
Total cost = $12.95 + $3.79 + $1.01
Total cost = $17.75
Calculate Change
Change = Carol's payment - Total cost
Change = $20 - $17.75
Change = [B]$2.25[/B]

Carrie had $32 when she got to the carnival. After riding 6 rides, she had $20 left. What was the pr

Carrie had $32 when she got to the carnival. After riding 6 rides, she had $20 left. What was the price for each ride?
If Carrie had $20 left, then the rides cost:
$32 - $20 = 12
Price per ride = Cost per all rides / Total Rides
Price per ride = 12/6
Price per ride = [B]2[/B]

cereal is on sale for 3.60 for a 9-ounce box. what is the price per ounce?

cereal is on sale for 3.60 for a 9-ounce box. what is the price per ounce?
price per ounce = Total cost / ounces
price per ounce = 3.60/9
price per ounce = [B]$0.40[/B]

Chain Discounts and Net Cost Price and Net Cost Equivalent

Free Chain Discounts and Net Cost Price and Net Cost Equivalent Calculator - Given a chain discount and an original price, this calculates the total discount and net cost price.

Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of f

Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Chang wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this.
We have [B]25f + 100c < 600[/B] as our inequality.

Charlie collects rare coins. Of his display cases, 3 cases contain 15 coins each and 4 cases contain

Charlie collects rare coins. Of his display cases, 3 cases contain 15 coins each and 4 cases contain 17 coins each. On Monday, Charlie bought 10 new coins for his collection. How many total coins does he have in his collection now?
We have cases * coins + extra coins:
3(15) + 4(17) + 10
45 + 68 + 10
[B]123 coins[/B]

Chicken is on sale for $3.90 per pound. If Ms.Gelllar buys 2.25 pounds of chicken, how much will she

Chicken is on sale for $3.90 per pound. If Ms.Gelllar buys 2.25 pounds of chicken, how much will she spend? round to the nearest penny and show your work
Total spend = Cost per pound * Number of pounds
Total spend = $3.90 * 2.25 pounds
Total spend = [B]$8.78[/B] (rounded to 2 digits)

Cholesterol

Free Cholesterol Calculator - Solves for each of the 4 following cholesterol equation items:

1) Total Cholesterol

2) High Density Lipoproteins (HDL)*Good Cholesterol*

3) Low Density Lipoproteins (LDL)*Bad Cholesterol*

4) Triglycerides

1) Total Cholesterol

2) High Density Lipoproteins (HDL)

3) Low Density Lipoproteins (LDL)

4) Triglycerides

Christopher has $25 000 to invest. He finds a bank who will pay an interest rate of 5.65% p.a compou

Christopher has $25 000 to invest. He finds a bank who will pay an interest rate of 5.65% p.a compounded annually. What will the total balance be after 6 years?
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=25000&nval=6&int=5.65&pl=Annually']compound interest balance calculator[/URL], we get:
[B]34,766.18[/B]

Claire bought 180 candies and 140 pens for goody bags for her birthday. What is the largest number o

Claire bought 180 candies and 140 pens for goody bags for her birthday. What is the largest number of goody bags that Claire can make so that each goody bag has the same number of candies and the same number of pens? (All candies and pens should be used.)
We want the greatest common factor of 180 and 140. When we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=140&num2=180&num3=&pl=GCF+and+LCM']run GCF(180,140) in our calculator[/URL], we get 20.
We divide our total candies and total pens by our GCF. So each bag has the following:
Candies: 180/20 = [B]9 candies[/B]
Pens: 140/20 = [B]7 pens[/B]

Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends,

Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends, he will have 5 cards left. If he gives 8 cards to each of his friends, he will need 7 more cards. How many friends is the giving the cards to?
Let the number of friends Clark gives his cards to be f. Let the total amount of cards he gives out be n. We're given 2 equations:
[LIST=1]
[*]6f + 5 = n
[*]8f - 7 = n
[/LIST]
Since both equations equal n, we set these equations equal to each other
6f + 5 = 8f - 7
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=6f%2B5%3D8f-7&pl=Solve']type this equation into our search engine[/URL] and we get:
f = [B]6
[/B]
To check our work, we plug in f = 6 into each equation:
[LIST=1]
[*]6(6) + 5 = 36 + 5 = 41
[*]8(6) - 7 = 48 - 7 = 41
[/LIST]
So this checks out. Clark has 41 total cards which he gives to 6 friends.

Coin Combinations

Free Coin Combinations Calculator - Given a selection of coins and an amount, this determines the least amount of coins needed to reach that total.

Coin Total Word Problems

Free Coin Total Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value with a certain amount more or less of one coin than another

Coin Values

Free Coin Values Calculator - This calculates the total value of a given amount of:

* Pennies

* Nickels

* Dimes

* Quarters

* Half-Dollars

* Dollars

* Pennies

* Nickels

* Dimes

* Quarters

* Half-Dollars

* Dollars

Coin Word Problems

Free Coin Word Problems Calculator - This word problem lesson solves for a quantity of two coins totaling a certain value

Cole and Finn are roommates. They paid three months rent and a $200 security deposit when they signe

Cole and Finn are roommates. They paid three months rent and a $200 security deposit when they signed the lease. In total, they paid $1,850. What is the rent for one month? Write an equation and solve it.
Equation, let m = rent for one month
3m + 200 = 1,850
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3m%2B200%3D1850&pl=Solve']Equation Solver[/URL], we get [B]m = 550[/B].

Computers R US was selling laptops that had 4GB of memory for $495. You can buy additional memory fo

Computers R US was selling laptops that had 4GB of memory for $495. You can buy additional memory for $97 per GB. If your grandfather gave you $980 to buy a laptop and additional memory, how much memory can you get?
Figure out remaining money total after buying the laptop
[LIST=1]
[*]4GB: 980 - 495 = 485
[*]485/97 = 5 GB
[*]4GB + 5GB = [B]9GB[/B]
[/LIST]

Concert tickets cost $14.95 each. Which expression represents the total cost of 25 tickets?

Concert tickets cost $14.95 each. Which expression represents the total cost of 25 tickets?
Calculate Total Cost:
Total Cost = Cost Per Ticket * Number of Tickets
Total Cost = $14.95 * 25
Total Cost = [B]$373.75[/B]

Connor bought 386.21 pounds of peanuts and 331.28 pounds of raisins. How many pounds of snacks did h

Connor bought 386.21 pounds of peanuts and 331.28 pounds of raisins. How many pounds of snacks did he buy in all?
Since peanuts [U]and[/U] raising are both snacks, we [URL='http://www.mathcelebrity.com/longdiv.php?num1=386.21&num2=331.28&pl=Add']add the weights[/URL].
Total pounds = 386.21 + 331.28
Total pounds = [B]717.49[/B]

Cost Revenue Profit

Free Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

Counting with Groups of 10 and Leftovers

Free Counting with Groups of 10 and Leftovers Calculator - This calculator finds the total using groups of tens and leftover values.

Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total

Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total produced in both countries is 40,000,000 carats, find the amount produced in each country.
Set up our two given equations:
[LIST=1]
[*]A = 7B
[*]A + B = 40,000,000
[/LIST]
Substitute (1) into (2)
(7B) + B = 40,000,000
Combine like terms
8B = 40,000,000
Divide each side by 8
[B]B = 5,000,000[/B]
Substitute this into (1)
A = 7(5,000,000)
[B]A = 35,000,000[/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]

Dakota needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week deliveri

Dakota needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week delivering newspapers. How many weeks will Dakota have to deliver papers to have enough money to buy the bicycle?
Let w be the number of weeks of delivering newspapers. We have the equation:
15w + 40 = 400
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=15w%2B40%3D400&pl=Solve']type this equation into our search engine[/URL] and we get:
w = [B]24[/B]

Dale has a bookcase with d shelves. There are 14 books on each shelf. Using d, write an expression f

Dale has a bookcase with d shelves. There are 14 books on each shelf. Using d, write an expression for the total number of books.
We multiply the number of shelves by the number of books per shelf.
[B]14d[/B]

Dan earns £9.80 per hour. How much will he earn for 8 hours work?

Dan earns £9.80 per hour. How much will he earn for 8 hours work?
Calculate Total Earnings
Total Earnings = Hourly Rate * Number of Hours
Total Earnings = £9.80 * 8
Total Earnings = [B]£78.40[/B]

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the fries contain 15 grams of fat and the shake contains 9 grams of fat, how many burgers, at 17 grams of fat each, can Dan add to his fries and milkshake if he wants to keep the total fat content of his meal no greater than 69 grams?
His original meal is 1 fry and 1 shake. This contains 15 + 9 = 24 grams of fat.
To limit his meal to 69 grams of fat, he has 69 - 24 = 45 grams of fat left over.
Therefore, he can consume:
17b <= 45 where b is the number of burgers
Dividing by 17, we get b = 2.65. Since he does not want to go over 45, he can eat 2 burgers.

Dan makes 9 dollars for each hour of work. Write an equation to represent his total pay p after work

Dan makes 9 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.
We know that pay (p) on an hourly basis (h) equals:
p = Hourly Rate * h
We're given an hourly rate of 9, so we have:
p = [B]9h[/B]

Dane wrote the letters of “NEW YORK CITY” on cards and placed them in a hat. What is the probability

Dane wrote the letters of “NEW YORK CITY” on cards and placed them in a hat. What is the probability that he will draw the letter “Y” out of the hat?
New York City has 11 letters.
Our probability of drawing a Y is denoted as P(Y):
P(Y) = Number of Y's / Total Letters
P(Y) = [B]2/11[/B]

Daniel is 6cm taller than Kamala. If their total height is 368cm, how tall is Kamala?

Daniel is 6cm taller than Kamala. If their total height is 368cm, how tall is Kamala?
Let Daniel's height be d. Let Kamala's height be k. We're given two equations:
[LIST=1]
[*]d = k + 6
[*]d + k = 368
[/LIST]
Substitute equation (1) into equation (2) for d:
k + 6 + k = 368
To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=k%2B6%2Bk%3D368&pl=Solve']type this equation into our search engine[/URL] and we get:
k = [B]181[/B]

Daniel pays $10 to get into the parking lot and will pay a fee of $2 per hour his car will be left i

Daniel pays $10 to get into the parking lot and will pay a fee of $2 per hour his car will be left in the parking lot. He ending up paying a total of $23 for parking. How many hours was Daniels car left in the parking lot?
Calculate the amount of fees for hours:
Fees for hours = Total Bill - Entrance fee
Fees for hours = 23 - 10
Fees for hours = 13
Calculate the number of hours Daniel parked:
Number of hours = Fees for hours / Hourly Rate
Number of hours = 13/2
Number of hours = [B]6.5[/B]

Danny buys 5 books at $34 each and pays for them with 10-dollar bills. How many $10 bills did it tak

Danny buys 5 books at $34 each and pays for them with 10-dollar bills. How many $10 bills did it take?
Calculate his total bill:
Total bill = Number of books * cost per book
Total bill = 5 * 34
Total bill = 170
Now calculate the number of 10-dollar bills he used:
10-dollar bills used = Total bill / 10
10-dollar bills used = 170/10
10-dollar bills used = [B]17[/B]

Danny learns 2 new appetizer recipes during each week of culinary school. After 9 weeks of culinary

Danny learns 2 new appetizer recipes during each week of culinary school. After 9 weeks of culinary school, how many total appetizer recipes will Danny know?
2 appetizers per week * 9 weeks = [B]18 recipes[/B]

Dave rented a limousine for his wife's birthday. The hourly rate is $60. They used the limousine for

Dave rented a limousine for his wife's birthday. The hourly rate is $60. They used the limousine for 4 hours, plus Dave gave the driver a 20% tip. How much did he spend in total for the hourly charges plus tip?
Hourly Spend = $60 * 4 = $240
Calculate 20% tip
0.2 * $240 = $48
Calculate total:
$240 + 48 = [B]$288[/B]

David had 20 pencils. 5 of them are green and 15 are purple. What percentage of pencils were gr

David had 20 pencils. 5 of them are green and 15 are purple. What percentage of pencils were green?
Percentage of Green Pencils = 100* Green Pencils / Total Pencils
Percentage of Green Pencils = 100* 5/20
Percentage of Green Pencils = 500 / 20
Percentage of Green Pencils = [B]25%[/B]

David roller skates for 3 1/3 hours with a constant speed of 24 km/h and then for another 1 hour 10

David roller skates for 3 1/3 hours with a constant speed of 24 km/h and then for another 1 hour 10 minutes with constant speed of 12 km/h. What distance did he go?
Distance = Rate x Time
[U]Part 1 of his trip:[/U]
D1 = R1 x T1
D1 = 3 & 1/3 hours * 24 km/h
D1 = 80 km
[U]Part 2 of his trip:[/U]
D2 = R2 x T2
D2 = 1 & 1/6 hours * 12 km/h (Note, 10 minutes = 1/6 of an hour)
D2 = 14 km
[U]Calculate Total Distance (D)[/U]
D = D1 + D2
D = 80 + 14
D = [B]94 km[/B]

Deanna has 5-cent stamps and 10-cent stamps. If she has 100 total stamps, what is the value of the s

Deanna has 5-cent stamps and 10-cent stamps. If she has 100 total stamps, what is the value of the stamps? Call the 5-cent stamps n.
Value of 5-cent stamps
0.05n
Number of 10 cent stamps is:
100 - n
Value is 0.10(100 - n) = 10 - 0.10n
Add them both:
10 - 0.10n + 0.05n
[B]10 - 0.05n[/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]

Del and his 5 friends eat 4 pizzas. If each has the same amount and there is 1/4 of a pizza left ove

Del and his 5 friends eat 4 pizzas. If each has the same amount and there is 1/4 of a pizza left over, how much did each person eat?
This means 4 full pizzas - 1/4 of a pizza = 3 & 3/4 pizzas eaten
Del and his 5 friends means 6 people total. Since they ate equal amounts, we divide pizzas eaten by total people:
3 & 3/4 / 6
Convert 3 & 3/4 to a mixed fraction:
(4*3 + 3)/4 = 15/4
15/4/6
Divide by a fraction is the same as multiply by a reciprocal:
15/4 * 1/6 = [B]15/24 pizzas per person[/B]

Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5

Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5 percent sales tax, how much change would she receive from a $10 bill
1. Change = $10 - Total Bill
Total Bill = (Soda + Candy Bar + Bag of Chips) * 1.035
Total Bill = ($0.90 + $1.20 + $2.90) * 1.035
Total Bill = $5 * 1.035
2. Total Bill = $5.18
Plug Equation (2) into Equation (1), we have:
Change = $10 - $5.18
Change = [B]$4.82[/B]

Denise is packaging pencils for an art class. If she has 204 pencils and she puts 12 pencils into ea

Denise is packaging pencils for an art class. If she has 204 pencils and she puts 12 pencils into each box, how many boxes will Denise need?
Total Boxes = Total Pencils / pencils per box
Total Boxes = 204/12
Total Boxes = [B]17 boxes[/B]

Dennis was getting in shape for a marathon. The first day of the week he ran n miles. Dennis then ad

Dennis was getting in shape for a marathon. The first day of the week he ran n miles. Dennis then added a mile to his run each day. By the end of the week (7 days), he had run a total of 70 miles. How many miles did Dennis run the first day?
Setup distance ran for the 7 days:
[LIST=1]
[*]n
[*]n + 1
[*]n + 2
[*]n + 3
[*]n + 4
[*]n + 5
[*]n + 6
[/LIST]
Add them all up:
7n + 21 = 70
Solve for [I]n[/I] in the equation 7n + 21 = 70
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 21 and 70. To do that, we subtract 21 from both sides
7n + 21 - 21 = 70 - 21
[SIZE=5][B]Step 2: Cancel 21 on the left side:[/B][/SIZE]
7n = 49
[SIZE=5][B]Step 3: Divide each side of the equation by 7[/B][/SIZE]
7n/7 = 49/7
n =[B] 7
[URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B21%3D70&pl=Solve']Source[/URL][/B]

Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse

Derek must choose a 4 digit PIN. Each Digit can be chosen from 0 to 9. Derek does not want to reuse any digits. He also only wants an even number that begins with 5. How many possible PINS could he choose from?
[LIST=1]
[*]First digit must begin with 5. So we have 1 choice
[*]We subtract 1 possible digit from digit 3 to have 8 - 1 = 7 possible digits
[*]This digit can be anything other than 5 and the even number in the next step. So we have 0-9 is 10 digits - 2 = 8 possible digits
[*]Last digit must end in 0, 2, 4, 6, 8 to be even. So we have 5 choices
[/LIST]
Our total choices from digits 1-4 are found by multiplying each possible digit choice:
1 * 7 * 8 * 5 = [B]280 possible PINS[/B]

Dick invested $9538 in an account at 10% compounded annually. Calculate the total investment after

Dick invested $9538 in an account at 10% compounded annually. Calculate the total investment after 10 years. Round your answer to the nearest penny if necessary.
Annual compounding means we don't need to make adjustments to interest rate per compounding period.
[URL='https://www.mathcelebrity.com/compoundint.php?bal=9538&nval=10&int=10&pl=Annually']Using our compound interest calculator[/URL], we get our new balance after 10 years of:
[B]$24,739.12[/B]

Dominic bought 3 bags of beans. There are b beans in each bag.

Dominic bought 3 bags of beans. There are b beans in each bag.
Total beans = Bags of beans * beans per bag
Total beans = [B]3b[/B]

Dora has $35 saved. She earns $9.50 per hour at her job. How many hours must she work to have a tota

Dora has $35 saved. She earns $9.50 per hour at her job. How many hours must she work to have a total of $358 in her savings?
Subtract the existing savings from the desired savings to see what we have left:
358 - 35 = 323
Now, at 9.50 per hour, how many hours of work does she need to get 323?
Let h be the number of hours. We have:
9.50h = 323
[URL='http://www.mathcelebrity.com/1unk.php?num=9.50h%3D323&pl=Solve']Running this problem through our search engine[/URL], we get
[B]h = 34[/B]

During a game, a basketball team scored 38 points worth of two-pointers, 33 points worth of three-po

During a game, a basketball team scored 38 points worth of two-pointers, 33 points worth of three-pointers, and 8 points worth of free throws. How many shots did the basketball team make during the game? shots (Hint: A free throw is worth one point).
[U]Calculate two-point shots:[/U]
Two-point shots = Two Pointers / 2
Two-point shots = 38/2
Two-point shots = 19
[U]Calculate three-point shots:[/U]
Three-point shots = Three Pointers / 2
Three-point shots = 33/3
Three-point shots = 11
[U]Calculate free-throw shots:[/U]
Free throw shots = Free throws / 1
Free throw shots = 8/1
Free throw shots = 8
[U]Calculate total shots:[/U]
Total shots = Two-point shots + three-point shots + free throws
Total shots = 19 + 11 + 8
Total shots = [B]38[/B]

During a recent season Miguel Cabrera and Mike Jacobs hit a combined total of 46 home runs. Cabrera

During a recent season Miguel Cabrera and Mike Jacobs hit a combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs how many home runs did each player hit
Let c be Miguel Cabrera's home runs and j be Mike Jacobs home runs. We are given two equations:
[LIST=1]
[*]c + j = 46
[*]c = j + 6
[/LIST]
Substitute (2) into (1)
(j + 6) + j = 46
Combine like terms:
2j + 6 = 46
[URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B6%3D46&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]j = 20[/B].
Substitute this into equation (2), we have:
c = 20 + 6
[B]c = 26
[/B]
Therefore, Mike Jacobs hit 20 home runs and Miguel Cabrera hit 26 home runs.

During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also wor

During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours, t, must you work as a landscaper?
[U]Calculate your gas station salary:[/U]
Gas Station Salary = Hours Worked * Hourly Rate
Gas Station Salary = 30 * $8.75
Gas Station Salary = $262.50
[U]Now subtract this from the desired weekly earnings of $400[/U]
$400 - 262.50 = $137.50
The landscaper makes $11 per hour. And they want to make $137.50 from landscaping. So we have the following equation:
11t = 137.50
Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=11t%3D137.50&pl=Solve']equation calculator[/URL], and we get t = 12.5 hours.

Dwayne earn $6 for each hour of yard work. After doing a total of 3 hours of yard work, how much mon

Dwayne earn $6 for each hour of yard work. After doing a total of 3 hours of yard work, how much money will Dwayne have earned?
We're given the hourly earnings equation below:
Hourly Earnings = Hourly Rate * hours worked
Hourly Earnings = $6 * 3
Hourly Earnings = [B]$18[/B]

Each brick is 14 inches long, 8 inches wide, and 5 inches tall.if they used 16,800 in3 of concrete,

Each brick is 14 inches long, 8 inches wide, and 5 inches tall.if they used 16,800 in3 of concrete, how many bricks did they make?
Volume of a brick (V) is:
V = l * w * h
Plugging in our brick measurements, we get:
V = 14 * 8 * 5
V = 560
Calculate number of bricks:
Number of Bricks = Total Volume / Volume of one Brick
Number of Bricks = 16,800/560
Number of Bricks =[B]30[/B]

Each calendar will selll for $5.00 each. Write an equation to model the total income,y, for selling

Each calendar will selll for $5.00 each. Write an equation to model the total income,y, for selling x calendars
income (y) = Price * Quantity
[B]y = 5x[/B]

each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total nu

each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total number of desks in the school was 543. How many classrooms does the school have?
Let d be the number of desks per classroom. We're given an equation:
26d + 75 = 543
To solve for d, [URL='https://www.mathcelebrity.com/1unk.php?num=26d%2B75%3D543&pl=Solve']type this equation into our search engine[/URL] and we get:
d = [B]18[/B]

Each pair of skates has 8 wheels.if the skating rink has 87 pairs of skates. How many wheels are at

Each pair of skates has 8 wheels.if the skating rink has 87 pairs of skates. How many wheels are at the rink?
Total Wheels = Pairs of Skates * 8 wheels per pair
Total Wheels = 87 * 8
Total Wheels = [B]609[/B]

Each tree in an orchard containing 2,650 trees requires 210 grams of fertiliizer. At $1.25 per kilog

Each tree in an orchard containing 2,650 trees requires 210 grams of fertiliizer. At $1.25 per kilogram of fertilizer, how much does it cost to fertilize the orchard?
[U]Calculate the total fertilizer needed:[/U]
Total fertilizer needed = Number of trees * grams of fertilizer per tree
Total fertilizer needed = 2650 * 210
[URL='https://www.mathcelebrity.com/longdiv.php?num1=2650&num2=210&pl=Multiply']Total fertilizer needed[/URL] = 556500 grams
[U]1 kilogram = 1000 grams, so we convert our 556500 grams to kilograms:[/U]
kilograms of fertilizer = grams of fertilizer / 1000
kilograms of fertilizer = 556500/1000
kilograms of fertilizer = 556.5
[U]Calculate fertilizer cost:[/U]
Fertilizer cost = kilograms of fertilizer * cost per kilogram
Fertilizer cost = 556.5 * 1.25
Fertilizer cost = [B]695.63[/B]

Eight students made 272.00 mowing lawns. How much did each student make?

Eight students made 272.00 mowing lawns. How much did each student make?
Earnings per Student = Total Earnings / Number of Students
Earnings per Student = 272/8
Earnings per Student = [B]34[/B]

Electrons have a charge of -1. Protons have a charge of 1. The total charge of an atom is the sum of

Electrons have a charge of -1. Protons have a charge of 1. The total charge of an atom is the sum of its electron charges and proton charges. Find the total charge of an atom with 24 protons and 32 electrons
We use sign operations to get:
+24 - 32 = [B]-8[/B]

Elli is purchasing 2.75 pounds of jelly beans which are priced at 4.85 per pound. How much change sh

Elli is purchasing 2.75 pounds of jelly beans which are priced at 4.85 per pound. How much change should she get back from a 20?
The total bill is 4.85 per pound * 2.75 pounds = 13.34
Her change from a 20 is 20 - 13.34 = [B]6.66[/B].

Elsa took a total of 25 quizzes over the course of 5 weeks. After attending 8 weeks of school this q

Elsa took a total of 25 quizzes over the course of 5 weeks. After attending 8 weeks of school this quarter, how many quizzes will Elsa have taken in total? Assume the relationship is directly proportional.
Set up a proportion of quizzes to weeks where q is the number of quizzes taken in 8 weeks. We have:
25/5 = q/8
We [URL='https://www.mathcelebrity.com/prop.php?num1=25&num2=q&den1=5&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search engine[/URL] and we get:
q = [B]40[/B]

Eric is playing football and loses 7 yards per play how many plays does it take for him to lose 21 y

Eric is playing football and loses 7 yards per play how many plays does it take for him to lose 21 yards total
Total plays = Total yards / Yards per play
Total plays = 21/7
Total plays = [B]3[/B]

Erica earned 771.84 working as a carpenter. She worked for 8 days. How much did she earn per day?

Erica earned 771.84 working as a carpenter. She worked for 8 days. How much did she earn per day?
Daily earnings = Total Earnings / Days Worked
Daily earnings = 771.84 / 8
Daily earnings = [B]96.48[/B]

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an eve

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an even number on one cube and a prime number on the other?
P(Even on first cube) = (2,4,6) / 6 total choices
P(Even on first cube) = 3/6
P(Even on first cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
P(Prime on second cube) = (2,3,5) / 6 total choices
P(Prime on second cube) = 3/6
P(Prime on second cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL]
Since each event is independent, we have:
P(Even on the first cube, Prime on the second cube) = P(Even on the first cube) * P(Prime on the second cube)
P(Even on the first cube, Prime on the second cube) = 1/2 * 1/2
P(Even on the first cube, Prime on the second cube) = [B]1/4[/B]

Farah rolls a fair dice and flips a fair coin. What is the probability of obtaining a 5 and a head?

Farah rolls a fair dice and flips a fair coin. What is the probability of obtaining a 5 and a head? Give your answer in its simplest form.
Probability of a 5 is 1/6
Probability of a head is 1/2
Since each event is independent, we get the total probability by multiplying both together:
P(5,H) = 1/6 * 1/2
P(5,H) = [B]1/12[/B]

final cost for a hair cut is 22.00 the tax is 2.00 what is the tax percentage

final cost for a hair cut is 22.00 the tax is 2.00 what is the tax percentage
Calculate Tax Percentage
Tax Percentage = 100% * Tax / Total Bill
Tax Percentage = 100% * 2/22
Tax Percentage = 100% * 1/11
Tax Percentage = [B]9.09%[/B]

Finance

1. Spend 8000 on a new machine. You think it will provide after tax cash inflows of 3500 per year for the next three years. The cost of funds is 8%. Find the NPV, IRR, and MIRR. Should you buy it?
2. Let the machine in number one be Machine A. An alternative is Machine B. It costs 8000 and will provide after tax cash inflows of 5000 per year for 2 years. It has the same risk as A. Should you buy A or B?
3. Spend 100000 on Machine C. You will need 5000 more in net working capital. C is three year MACRS. The cost of funds is 8% and the tax rate is 40%. C is expected to increase revenues by 45000 and costs by 7000 for each of the next three years. You think you can sell C for 10000 at the end of the three year period.
a. Find the year zero cash flow.
b. Find the depreciation for each year on the machine.
c. Find the depreciation tax shield for the three operating years.
d. What is the projects contribution to operations each year, ignoring depreciation effects?
e. What is the cash flow effect of selling the machine?
f. Find the total CF for each year.
g. Should you buy it?

find the probability of drawing a 4 or an ace

find the probability of drawing a 4 or an ace.
In a 52 card deck, there are 4 (4's) and 4 (Aces), for a total of 8 cards:
The probability is 8 cards / 52 total cards:
8/52 using our s[URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F52&frac2=3%2F8&pl=Simplify']implify fractions calculator[/URL] = [B]2/13[/B]

Find the total coast of four nights lodging at $62.00 per night with 8 1/2% sales tax.

Find the total coast of four nights lodging at $62.00 per night with 8 1/2% sales tax.
[U]Calculate Total lodging cost[/U]
Total lodging cost = Nightly Rate * Number of Nights
Total lodging cost = 62 * 4
Total lodging cost = 248
[U]Calculate total bill with tax[/U]
Total bill with tax = Total bill * (1 + sales tax percent)
Total bill with tax = 248 * (1 + 0.85) <-- 8 1/2% = 0.085 as a decimal
Total bill with tax = 248 * 1.085
Total bill with tax =[B] $269.08[/B]

flip 7 coins How many total outcomes are there

flip 7 coins How many total outcomes are there
A flip of a coin has 2 outcomes, heads or tails. Since each outcome is independent of the other outcomes, we multiply each flip by 2 outcomes:
Total outcomes = 2 * 2 * 2 * 2 * 2 * 2 * 2
Total outcomes = 2^7
Total outcomes = [B]128[/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 is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find

Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find a linear function that expresses the total cost C for plumbing services for h hours.
Cost functions include a flat rate and a variable rate. The flat rate is $35 and the variable rate per hour is 15. The cost function C(h) where h is the number of hours Frank works is:
[B]C(h) = 15h + 35[/B]

From a regular deck of 52 playing cards, you turn over a 6 and then a 7. What is the probability tha

From a regular deck of 52 playing cards, you turn over a 6 and then a 7. What is the probability that the next card you turn over will be a face card?
Key phrases: 52 card standard deck so you know there's no tricks or missing cards.
[U]Calculate the number of face cards in a standard 52 card deck[/U]
First, we know that face cards = (J, K, Q)
We also know that there are 4 suits (Hearts, Diamonds, Spades, Clubs)
Total Face Cards = 3 face card types * 4 possible suits = 12 face cards
[U]Calculate total face down cards[/U]
First card, you turn over a 6
Next card, you turn over a 7
This means, we have 52 cards - 2 cards from the draws = 50 cards left in the deck which are face down.
P(Face Card) = Total Face Cards / Total Cards in the Deck Face Down
P(Face Card) = 12/50
Simplifying this fraction [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F50&frac2=3%2F8&pl=Simplify']using our math engine[/URL], we get:
P(Face Card) = [B]6/25[/B]

Fundamental Rule of Counting

Free Fundamental Rule of Counting Calculator - Given a set of items, this calculates the total number of groups/choices that can be formed using the rule of product.

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a t

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a total of 25 apples.
Let George's apples be g. Let Sarah's apples be s. We're give two equations:
[LIST=1]
[*]s = 4g
[*]g + s = 25
[/LIST]
Substitute equation (1) into equation (2) for s:
g + 4g = 25
If [URL='https://www.mathcelebrity.com/1unk.php?num=g%2B4g%3D25&pl=Solve']we plug this equation into our search engine[/URL] and solve for g, we get:
g = [B]5[/B]
Now substitute this into equation 1 for g = 5:
s = 4(5)
s = [B]20[/B]
[B]So George has 5 apples and Sarah has 20 apples[/B]

Georgina has 9 bags of shaved coconuts. If each bag weighs 1/2 pounds what is the total weight of th

Georgina has 9 bags of shaved coconuts. If each bag weighs 1/2 pounds what is the total weight of the bags?
We take 9 bags * 1/2 pound per bag = [B]4.5 total pounds[/B].

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2

Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2 equations.
Let g be the number of German states. Let a be the number of Austrian states. We're given two equations:
[LIST=1]
[*]a + g = 25
[*]g = a + 7
[/LIST]
To solve this system of equations, we substitute equation (2) into equation (1) for g:
a + (a + 7) = 25
Combine like terms:
2a + 7 = 25
To solve for a, we[URL='https://www.mathcelebrity.com/1unk.php?num=2a%2B7%3D25&pl=Solve'] type this equation into our search engine[/URL] and we get:
[B]a = 9[/B]
To solve for g, we plug in a = 9 into equation (2):
g = 9 + 7
[B]g = 16[/B]

Gina earns $68.75 for 5 hours of tutoring how much did she earn per minute

Gina earns $68.75 for 5 hours of tutoring how much did she earn per minute
1 hour = 60 minutes
5 hours = 60 * 5
5 hours = 300 minutes
Cost per minute = Earnings / Total Minutes
68.75/300 minutes
[B]23 cents per minute[/B]

Golden Ratio

Free Golden Ratio Calculator - Solves for 2 out of the 3 variables for a segment broken in 2 pieces that satisfies the Golden Ratio (Golden Mean).

(a) Large Segment

(b) Small Segment

(a + b) Total Segment

(a) Large Segment

(b) Small Segment

(a + b) Total Segment

Grayson took a total of 16 quizzes over the course of 8 weeks. How many weeks of school will Grayson

Grayson took a total of 16 quizzes over the course of 8 weeks. How many weeks of school will Grayson have to attend this quarter before he will have taken a total of 20 quizzes? Assume the relationship is directly proportional.
Set up a proportion of quizzes to weeks, where w is the number of weeks for 20 quizzes:
16/8 = 20/w
[URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=20&den1=8&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get:
w = [B]10[/B]

Gregg has 8 cards.Half red,half black. He picks 2 cards from the deck.What is the probability both o

Gregg has 8 cards.Half red,half black. He picks 2 cards from the deck.What is the probability both of them are red?
Half means 4 cards are red and 4 cards are black.
The first draw probability of red is:
4 total red cards out of 8 total cards = 4/8.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F8&frac2=3%2F8&pl=Simplify']Simplified, this is[/URL] 1/2
The second draw is 3 total red cards out of 7 remaining cards. Since 1 red was drawn (4 - 1) = 3 reds left and 1 card was drawn (8 -1) = left
3/7
Since each draw is independent, we multiply the probabilities:
1/2 * 3/7 = [B]3/14[/B]

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think

Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think of the monthly charges paid at the end of the month.) Enter the number of months it will take for the total cost for both gyms to be equal.
Gym A cost function C(m) where m is the number of months:
C(m) = Monthly charge * months + Joining Fee
C(m) = 35m + 75
Gym B cost function C(m) where m is the number of months:
C(m) = Monthly charge * months + Joining Fee
C(m) = 60m
Set them equal to each other:
35m + 75 = 60m
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=35m%2B75%3D60m&pl=Solve']we type this equation into our search engine[/URL] and get:
m = [B]3[/B]

Hanna cooked 5 pizzas. She sliced each pizza into eighths. How many slices of pizza does she have in

Hanna cooked 5 pizzas. She sliced each pizza into eighths. How many slices of pizza does she have in total?
5 pizzas times 8 slices per pizza = [B]40 slices[/B]

Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $1

Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $2.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
Happy Paws Cost: C = 16 + 1.5h
Woof Watchers: C = 11 + 2.75h
Setup the equation where there costs are equal
16 + 1.5h = 11 + 2.75h
Subtract 11 from each side:
5 + 1.5h = 2.75h
Subtract 1.5h from each side
1.25h = 5
Divide each side by 1.25
[B]h = 4[/B]

Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $1

Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $6.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
[B]Happy Paws cost equation:[/B]
5.50h + 19
[B]Woof Watchers cost equation:[/B]
6.75h + 11
[B]Set them equal to each other:[/B]
5.50h + 19 = 6.75h + 11
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=5.50h%2B19%3D6.75h%2B11&pl=Solve']equation solver[/URL], we get [B]h = 6.4[/B].

He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the deli

He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the delivery address. Write an equation that can be used to calculate the delivery price and the distance between the kitchen and the delivery address. Use your equation to calculate the total cost to deliver to someone 2.4km away
Let k be the number of kilometers between the kitchen and delivery address. Our Delivery equation D(k) is:
[B]D(k) = 2k + 1.50[/B]
The problem wants to know D(2.4):
D(2.4) = 2(2.4) + 1.50
D(2.4) = 4.8 + 1.50
D(2.4) = [B]$6.30[/B]

Hemisphere

Free Hemisphere Calculator - Calculates the base circumference, volume, curved surface area, base surface area, total surface area of a hemisphere with radius r

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

Here is Practical Explanation about Next Life, Purpose of Human Life, philosophical/religious facts,

Practical Explanation ( For Example ) :- `1st of all can you tell me every single seconds detail from that time when you born ?? ( i need every seconds detail ?? that what- what you have thought and done on every single second )
can you tell me every single detail of your `1 cheapest Minute Or your whole hour, day, week, month, year or your whole life ??
if you are not able to tell me about this life then what proof do you have that you didn't forget your past ? and that you will not forget this present life in the future ?
that is Fact that Supreme Lord Krishna exists but we posses no such intelligence to understand him.
there is also next life. and i already proved you that no scientist, no politician, no so-called intelligent man in this world is able to understand this Truth. cuz they are imagining. and you cannot imagine what is god, who is god, what is after life etc.
_______
for example :Your father existed before your birth. you cannot say that before your birth your father don,t exists.
So you have to ask from mother, "Who is my father?" And if she says, "This gentleman is your father," then it is all right. It is easy.
Otherwise, if you makes research, "Who is my father?" go on searching for life; you'll never find your father.
( now maybe...maybe you will say that i will search my father from D.N.A, or i will prove it by photo's, or many other thing's which i will get from my mother and prove it that who is my Real father.{ So you have to believe the authority. who is that authority ? she is your mother. you cannot claim of any photo's, D.N.A or many other things without authority ( or ur mother ).
if you will show D.N.A, photo's, and many other proofs from other women then your mother. then what is use of those proofs ??} )
same you have to follow real authority. "Whatever You have spoken, I accept it," Then there is no difficulty. And You are accepted by Devala, Narada, Vyasa, and You are speaking Yourself, and later on, all the acaryas have accepted. Then I'll follow.
I'll have to follow great personalities. The same reason mother says, this gentleman is my father. That's all. Finish business. Where is the necessity of making research? All authorities accept Krsna, the Supreme Personality of Godhead. You accept it; then your searching after God is finished.
Why should you waste your time?
_______
all that is you need is to hear from authority ( same like mother ). and i heard this truth from authority " Srila Prabhupada " he is my spiritual master.
im not talking these all things from my own.
___________
in this world no `1 can be Peace full. this is all along Fact.
cuz we all are suffering in this world 4 Problems which are Disease, Old age, Death, and Birth after Birth.
tell me are you really happy ?? you can,t be happy if you will ignore these 4 main problem. then still you will be Forced by Nature.
___________________
if you really want to be happy then follow these 6 Things which are No illicit s.ex, No g.ambling, No d.rugs ( No tea & coffee ), No meat-eating ( No onion & garlic's )
5th thing is whatever you eat `1st offer it to Supreme Lord Krishna. ( if you know it what is Guru parama-para then offer them food not direct Supreme Lord Krishna )
and 6th " Main Thing " is you have to Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare ".
_______________________________
If your not able to follow these 4 things no illicit s.ex, no g.ambling, no d.rugs, no meat-eating then don,t worry but chanting of this holy name ( Hare Krishna Maha-Mantra ) is very-very and very important.
Chant " hare krishna hare krishna krishna krishna hare hare hare rama hare rama rama rama hare hare " and be happy.
if you still don,t believe on me then chant any other name for 5 Min's and chant this holy name for 5 Min's and you will see effect. i promise you it works And chanting at least 16 rounds ( each round of 108 beads ) of the Hare Krishna maha-mantra daily.
____________
Here is no Question of Holy Books quotes, Personal Experiences, Faith or Belief. i accept that Sometimes Faith is also Blind. Here is already Practical explanation which already proved that every`1 else in this world is nothing more then Busy Foolish and totally idiot.
_________________________
Source(s):
every `1 is already Blind in this world and if you will follow another Blind then you both will fall in hole. so try to follow that person who have Spiritual Eyes who can Guide you on Actual Right Path. ( my Authority & Guide is my Spiritual Master " Srila Prabhupada " )
_____________
if you want to see Actual Purpose of human life then see this link : ( triple w ( d . o . t ) asitis ( d . o . t ) c . o . m {Bookmark it })
read it complete. ( i promise only readers of this book that they { he/she } will get every single answer which they want to know about why im in this material world, who im, what will happen after this life, what is best thing which will make Human Life Perfect, and what is perfection of Human Life. ) purpose of human life is not to live like animal cuz every`1 at present time doing 4 thing which are sleeping, eating, s.ex & fear. purpose of human life is to become freed from Birth after birth, Old Age, Disease, and Death.

Hero cards come in packs of 6. Max has 8 packs of hero cards. He decides to give as many of his frie

Hero cards come in packs of 6. Max has 8 packs of hero cards. He decides to give as many of his friends as he can 9 cards each. How many cards are left over after he does this?
Calculate the number of cards Max starts with:
8 packs * 6 cards per pack = 48 total cards
If he gives as many friends as he can 9 cards each, we want to know how many left over after giving as many friends as he can 9 cards. So we have:
[URL='https://www.mathcelebrity.com/modulus.php?num=48mod9&pl=Calculate+Modulus']48 mod 9[/URL] = [B]3 left over[/B]

High and Low Method

Free High and Low Method Calculator - Calculates the variable cost per unit, total fixed costs, and the cost volume formula

High-Low Method

Free High-Low Method Calculator - Calculates Variable Cost per Unit, Total Fixed Cost, and Cost Volume using the High-Low Method

How many 8$, tickets can I get for 100$

How many 8$, tickets can I get for 100$
Tickets = Total Money / price per ticket
Tickets = 100/8
Tickets = [B]12.5
[/B]
If the problem asks for a whole number, this means you cannot have a partial ticket. Therefore, we round down to [B]12 tickets[/B]

How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the b

How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the bag is 8 cents?
200 nickels has a value of 200 * 0.05 = $10.
Average value of coins is $10/200 = 0.05
Set up our average equation, where we have total value divided by total coins:
(200 * 0.05 + 0.1d)/(200 + d) = 0.08
Cross multiply:
16 + 0.08d = 10 + 0.1d
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=16%2B0.08d%3D10%2B0.1d&pl=Solve']equation solver[/URL], we get:
[B]d = 300[/B]

How many wheels would 9 tricycles have?

How many wheels would 9 tricycles have?
Each tricycle has 3 wheels, so the total wheels is found below:
Total Wheels = 3 wheels per tricycle * 9 tricycles
Total Wheels = [B]27[/B]

Hypergeometric Distribution

Free Hypergeometric Distribution Calculator - Calculates the probability of drawing x objects out of a subgroup of k with n possibilities in a total group of N using the hypergeometric distribution.

I bought four candles that cost 7.00, 8.00, 9.00, and 20.00. If I have a budget of $50, how much can

I bought four candles that cost 7.00, 8.00, 9.00, and 20.00. If I have a budget of $50, how much can I spend on the last candle?
[U]Add up your total spending:[/U]
7 + 8 + 9 + 20 = 44
[U]Determine your remaining budget:[/U]
Remaining Budget = Total Budget - Spending
Remaining Budget = 50 - 44
Remaining Budget = [B]$6.00[/B]

I had $21 to spend on two notebooks after buying them I had $13 how much did each notebook cost

I had $21 to spend on two notebooks after buying them I had $13 how much did each notebook cost?
If you had $13, leftover, this means you spent the following on notebooks:
$21 - $13 = $7
Cost per notebook = Total Notebook spend / Total Notebooks
Cost per notebook = $7/2
Cost per notebook = [B]$3.50[/B]

I have 20 bills consisting of $5 and $10. If the total amount of my money is $130, how many of each

I have 20 bills consisting of $5 and $10. If the total amount of my money is $130, how many of each bill do i have?
Let f be $5 bills and t be $10 bills, we have:
f + t = 20
5f + 10t = 130
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=f%2Bt%3D20&term2=5f+%2B+10t+%3D+130&pl=Cramers+Method']system of equation solver[/URL], we get:
[LIST]
[*][B]f = 14[/B]
[*][B]t = 6[/B]
[/LIST]

i have 25 pencil cases there are p pencils in each pencil case. how many pencils do i have altogethe

i have 25 pencil cases there are p pencils in each pencil case. how many pencils do i have altogether?
Total pencils = Number of cases * pencils per case
Total pencils = [B]25p[/B]

I have saved 24 to buy a game which is three-fourth of the total cost of the game how much does the

I have saved 24 to buy a game which is three-fourth of the total cost of the game how much does the game cost ?
Let the cost of the game be c. We're given:
3c/4 = 24
To solve this equation for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=24&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]32[/B]

I invest $3000 at 5% interest a year. So far I have made $600 with simple interest. How many years h

I invest $3000 at 5% interest a year. So far I have made $600 with simple interest. How many years have I been investing?
Simple interest is calculated using interest * principal.
We have 5% * 3000 = $150 interest per year
We take our $600 of total interest and divide it by our interest per year to get the total years:
$600 / $150 = [B]4 years[/B]

I need 3 cans of paint for each room and need to paint 20 rooms.

I need 3 cans of paint for each room and need to paint 20 rooms.
[U]Calculate the Total Paint Needed[/U]
Total Paint Needed = Total Rooms * Cans of paint per room
Total Paint Needed = 20 * 3
Total Paint Needed = [B]60[/B]

I only own blue blankets and red blankets. 8 out of every 15 blankets I have are red.

I only own blue blankets and red blankets. 8 out of every 15 blankets I have are red. If have i 45 blankets, how many are blue?
If 8 out of 15 blankets are red, then 15 - 8 = 7 are blue
So 7 out of every 15 blankets are blue.
Set up a proportion of blue blankets to total blankets where b is the number of blue blankets in 45 blankets
7/15 = b/45
Cross multiply:
If 2 proportions are equal, then we can do the following:
Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2
15b = 45 * 7
15b = 315
To solve for b, divide each side of the equation by 15:
15b/15 = 315/15
Cancel the 15's on the left side and we get:
b = [B]21[/B]

If 23.8% of a population is 8,212,000. What is the total population?

If 23.8% of a population is 8,212,000. What is the total population?
This can be written as [I]23.8% of x is 8212000
[/I]
We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=23.8&den1=8212000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type this expression into our search engine[/URL] and we get:
[B]1,954,456[/B]

If 27000 elephants are killed each year, how many elephants would be killed after 13 years

If 27000 elephants are killed each year, how many elephants would be killed after 13 years?
Total Elephants Killed = Elephants Killed per year * Total years
Total Elephants Killed = 27,000 * 13
Total Elephants Killed = [B]351,000[/B]

If 50 out of 250 people die. How many people died per 10 people

If 50 out of 250 people die. How many people died per 10 people
We set up a proportion of deaths to total people where d is the number of deaths for 10 people. We have:
50/250 = d/10
To solve this proportion for d, we [URL='https://www.mathcelebrity.com/prop.php?num1=50&num2=d&den1=250&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
d = [B]2[/B]

If 7 movie tickets cost $63 what is the unit price of the movie tickets?

If 7 movie tickets cost $63 what is the unit price of the movie tickets?
Unit Cost = Total Cost / Total Quantity
Unit Cost = 63/7
Unit Cost = [B]$9 per ticket[/B]

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his

If an employee starts saving with $750 and increases his savings by 8% each month, what will be his total savings after 10 months?
Set up the savings function S(m), where m is the number of months and I is the interest rate growth:
S(m) = Initial Amount * (1 + i)^m
Plugging in our number at m = 10 months we get:
S(10) = 750 * (1 + 0.08)^10
S(10) = 750 * 1.08^10
S(10) = [B]$1,619.19[/B]

If ben recently paid a $3.77 fine for a book that was 13 days late, what is the daily fine?

If ben recently paid a $3.77 fine for a book that was 13 days late, what is the daily fine?
Daily Fine = Total Fine / Number of Days
Daily Fine = $3.77 / 13 days
Daily Fine = [B]$0.29[/B]

If cement cost $4 per cubic foot, how much does a cubic yard of cement cost?

If cement cost $4 per cubic foot, how much does a cubic yard of cement cost?
There are 3 feet in a yard
3 x 3 x 3 = 27 cubic feet in a yard
Total cost = 27 cubic feet * $4 per cubic foot = [B]$108[/B]

if i had $667 and an apple cost $216, how many apples could i buy?

if i had $667 and an apple cost $216, how many apples could i buy?
Apples we can buy = Total money / Cost per apple
Apples we can buy = $667 / $216
Apples we can buy = 3.088
We round down to a full apple and get [B]3 apples[/B]

If I make 40,000 dollars every 15 minutes then how long will it take me to make a million

If I make 40,000 dollars every 15 minutes then how long will it take me to make a million
Let f be the number of fifteen minute blocks. We're given:
40000f = 1000000
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=40000f%3D1000000&pl=Solve']type this equation into our search engine[/URL] and we get:
f = 25
Total minutes = Fifteen minute blocks (f) * 15 minutes
Total minutes = 25 * 15
Total minutes = [B]375 minutes or 6 hours and 15 minutes[/B]

If jessica buys 2 bags of chips for $3.79 each, 6 candy bars for $1.15 each, and 3 steaks for $8.45

If jessica buys 2 bags of chips for $3.79 each, 6 candy bars for $1.15 each, and 3 steaks for $8.45 each. How much did she pay?
Calculate total cost per item, which is Price * Quantity
[LIST]
[*]Chips: $3.79 * 2 = $7.58
[*]Candy Bars: $1.15 * 6 = $6.90
[*]Steaks: $8.45 * 3 = $25.35
[/LIST]
Total Cost = Chips Cost + Candy Bars Cost + Steaks Cost
Total Cost = $7.58 + $6.90 + $25.35
Total Cost = [B]$39.83[/B]

If labor (x) costs $249 per unit, materials (y) cost $162 per unit, and capital (z) costs $ 7

If labor (x) costs $249 per unit, materials (y) cost $162 per unit, and capital (z) costs $ 77 per unit, write a function for total cost.
Total Cost = Labor Total Cost + Materials Total Cost + Capital Total Cost
Total Cost = [B]249x + 162y + 77z[/B]

If the max time that John can spend on Client A ($20/hr) in one week is 32 hours, and the min time i

If the max time that John can spend on Client A ($20/hr) in one week is 32 hours, and the min time is 8 hours, while the max time on Client B ($14/hr) is 8 hours and the min 5 hours, what is the RANGE (max, min) of total pay he can earn in one week (40 hours)
[LIST]
[*]Client A Minimum = 20 x 8 hours = $160
[*]Client A Maximum = 20 x 32 hours = $640
[*]Client B Minimum = 14 x 5 hours = $70
[*]Client B Maximum = 14 x 8 hours = $112
[/LIST]
[U]The Total Maximum Pay is found by adding Client A Maximum and Client B Maximum[/U]
Total Maximum = Client A Maximum + Client B Maximum
Total Maximum = 640 + 112
Total Maximum = 752
[U]The Total Minimum Pay is found by adding Client A Minimum and Client B Minimum[/U]
Total Minimum = Client A Minimum + Client B Minimum
Total Minimum = 160 + 70
Total Minimum = 230
[U]The Range is the difference between the Total maximum and the Total minimum[/U]
Range(Total Maximum, Total Minimum) = Total Maximum - Total Minimum
Range(752, 230) = 752 - 230
Range(752, 230) = [B]522[/B]

If the ratio of private school students to public school students in a city is 4 to 15 and there is

If the ratio of private school students to public school students in a city is 4 to 15 and there is a total of 18,601 students, how many students are in public schools?
Since 4 out of 15 are public school students, this means (15 - 4)/15 = 11/15 are public school students.
The total public school students are (11/15) * 18601 = 13,640.73. Rounded up, it is [B]13,641[/B].

If the temperature is dropping at a rate of 2° per hour, how many hours will take to drop 15°

If the temperature is dropping at a rate of 2° per hour, how many hours will take to drop 15°
Hours Needed = Total Temperature Drop / Drop per hour
Hours Needed = 15/2
Hours Needed = [B]7.5[/B]

If there are 7 bolts in a widget and 6 widgets in an appliance, how many bolts are in 20 appliances?

If there are 7 bolts in a widget and 6 widgets in an appliance, how many bolts are in 20 appliances?
Total Bolts = 7 bolts per widget * 6 widgets per appliance * 20 appliances
Total Bolts = 7 * 6 * 20 = [B]840[/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]

if you buy 50 bales of hay at $3.56 each, and then buy an additional 234 bales at $3.33 each, how mu

if you buy 50 bales of hay at $3.56 each, and then buy an additional 234 bales at $3.33 each, how much do you pay for the entire lot of 284 bales?
Since cost = price * quantity, we have:
Total lot cost = price(1) of hay * bales(1) of hay + price(2) of hay * bales(2) of hay
Total lot cost = 3.56 * 50 + 3.33 * 24
Total lot cost = 178 + 79.92
Total lot cost = [B]257.92[/B]

If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal in

If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal installments at 1.73% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
[U]Determine the monthly payment[/U]
The monthly payment is [B]$114.87[/B] using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=3059&av=&pmt=&n=36&i=1.73&check1=1&pl=Calculate']annuity calculator[/URL]
[U]Determine the total payments made[/U]
Total payment is 36 times $114.87 = $4,135.37
[U]Now determine the total interest paid[/U]
Take the total payments of $4,135.37 and subtract the original loan of $3,059 to get interest paid of [B]$1,076.37[/B]

If you how 8 dogs, how many total legs are there? How eyes and ears?

If you how 8 dogs, how many total legs are there? How eyes and ears?
[U]Calculate total dog legs:[/U]
Dog legs = 4 legs per dog * 8 dogs
Dog legs = [B]32 legs
[/B]
[U]Calculate total dog ears:[/U]
Dog ears = 2 ears per dog * 8 dogs
Dog ears = 16[B] ears
[/B]
[U]Calculate total dog eyes:[/U]
Dog eyes = 2 eyes per dog * 8 dogs
Dog eyes = 16 eyes

if you own 5 pants, 8 shirts, and 3 jackets how many outfits can you make wearing 1 of each item

if you own 5 pants, 8 shirts, and 3 jackets how many outfits can you make wearing 1 of each item?
Using the Fundamental Rule of counting, we have:
Total Pants * Total Shirts * Total Jackets
5 * 8 * 3
[B]120 [/B]

If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you

If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you to go 12 miles? (Assume no tip.)
a. Create an equation from the information above.
b. Identify the slope in the equation?
c. Calculate the total cost of the ride?
2. With the same charges as #1, how many miles could you go with $50, if you also gave a $7.50 tip? (Challenge Question! Hint, you only have a $50, exactly, with you
a. Cost Equation C(m) for m miles is as follows:
[B]C(m) = 1.57m + 5
[/B]
b.
Slope of the equation is the coefficient for m, which is [B]1.57
[/B]
c.
Total cost of the ride for m = 12 miles is:
C(12) = 1.57(12) + 5
C(12) = 18.84 + 5
C(12) = [B]23.84
[/B]
d.
If you give a 7.50 tip, we subtract the tip from the $50 to start with a reduced amount:
50 - 7.50 = 42.50
So C(m) = 42.50
1.57m + 5 = 42.50
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.57m%2B5%3D42.50&pl=Solve']type it in our search engine[/URL] and we get:
m = 23.89
Since we deal in full miles, we round our answer down to m = [B]23[/B]

if you worked for 3 hours and earned a total of $24, determine your hourly pay rate

if you worked for 3 hours and earned a total of $24, determine your hourly pay rate
Hourly Pay = Total Pay / Hours Worked
Hourly Pay = $24 /3
Hourly Pay = [B]$8 per hour[/B]

If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to e

If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to earn a total of $33.50 that week?
Let c be the number of chores. We're given the equation:
1.50c + 20 = 33.50
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.50c%2B20%3D33.50&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]9[/B]

In 2013, a local Dairy Queen had $502,000 in sales. In 2014, that same locations sales were up an ad

In 2013, a local Dairy Queen had $502,000 in sales. In 2014, that same locations sales were up an additional 43%. What was this Dairy Queens total sales in 2014?
2014 Sales = 2013 Sales * 1.43
2014 Sales = 502,000 * 1.43
2014 Sales = [B]717,860[/B]

In a car lot there are 38 rows with 25 parking spots in each row. How many parking spots are there?

In a car lot there are 38 rows with 25 parking spots in each row. How many parking spots are there?
Total parking spots = Number of Rows * Parking spots per row
Total parking spots = 38 * 25
Total parking spots = [B]950[/B]

In a certain lot, there are 16 white, 7 red, 8 blue, and 9 black cars. You randomly pick a set of ke

In a certain lot, there are 16 white, 7 red, 8 blue, and 9 black cars. You randomly pick a set of keys to one of the cars. What is the probability of choosing a set of keys to a blue car?
[U]Our total cars are:[/U]
Total Cars = White Cars + Red Cars + Blue Cars = Black Cars
Total Cars = 16 + 7 + 8 + 9
Total Cars = 40
P(Blue) = Blue Cars / Total Cars
P(Blue) = 8/40
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F40&frac2=3%2F8&pl=Simplify']fraction simplify calculator[/URL], we get:
P(Blue) = [B]1/5[/B]

in a class of 40 students 15 failed. How many passed

in a class of 40 students 15 failed. How many passed?
Passed = Total - Failed
Passed = 40 - 15
Passed = [B]25[/B]

In a sample of 80 beetles, 50 beetles had 4 spots each, and the rest had 6 spots each. What was the

In a sample of 80 beetles, 50 beetles had 4 spots each, and the rest had 6 spots each. What was the average number of spots per beetle? Show your work below.
Average spots per beetle = Total spots for all beetles / Total beetles
Average spots per beetle = (50(4) + 6(80 - 50))/80
Average spots per beetle =(200 + 6(30))/80
Average spots per beetle = (200 + 180)/80
Average spots per beetle = (380)/80
Average spots per beetle = [B]4.75 spots[/B]

In a school auditorium there are 36 seats in each row of seats. How many rows are needed for 716 stu

In a school auditorium there are 36 seats in each row of seats. How many rows are needed for 716 students to each have a seat?
Total Rows = total Students / Seats Per row
Total Rows = 716/36
Total Rows = 19.89
So we need [B]20 full rows[/B]

In a shipment of 330 animals, 125 were hogs, 68 were sheep, and the rest were cattle. Find the numbe

In a shipment of 330 animals, 125 were hogs, 68 were sheep, and the rest were cattle. Find the number of cattle in the shipment.
To find the rest (cattle), we subtract off the hogs and sheep from the total.
Cattle = Total Animals - Hogs - Sheep
Cattle = 330 - 125 - 68
[B]Cattle = 137[/B]

In one day, a store sells 14 pairs of jeans. The 14 jeans represent 20% of the total number of items

In one day, a store sells 14 pairs of jeans. The 14 jeans represent 20% of the total number of items sold that day. How many items did the store sell in one day? Explain or show how you got your answer.
14 = 20%s where s is the number of items sold in one day.
We can write 20% as 0.2, so we have:
0.2s = 14
[URL='https://www.mathcelebrity.com/1unk.php?num=0.2s%3D14&pl=Solve']Type this equation into the search engine[/URL], and we get:
s = [B]70[/B]

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game?
Let w be the winning team's points, and l be the losing team's points. We have two equations:
[LIST=1]
[*]w + l = 41
[*]w - l = 27
[/LIST]
Add the two equations:
2w = 68
Divide each side by 2
[B]w = 34[/B]
Substitute this into (1)
34 + l = 41
Subtract 34 from each side
[B]l = 7[/B]
Check your work:
[LIST=1]
[*]34 + 7 = 41 <-- check
[*]34 - 7 = 27 <-- check
[/LIST]
The final score of the game was [B]34 to 7[/B].
You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=w+%2B+l+%3D+41&term2=w+-+l+%3D+27&pl=Cramers+Method']simultaneous equation solver[/URL].

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 R

In the year 1980, Rick was twice as old as Nancy who was twice as old as Michael. In the year 1992 Ric, Nancy, and Michael ages added up to 78 years. How old was Ric in 1980?
Age in 1980:
[LIST]
[*]Let Michael's age be m
[*]Nancy's age is 2m
[*]Rick's age is 2 * 2m = 4m
[/LIST]
Age in 1992:
[LIST]
[*]Michael's age = m + 12
[*]Nancy's age is 2m + 12
[*]Rick's age is 2 * 2m = 4m + 12
[/LIST]
Total them up:
m + 12 + 2m + 12 + 4m + 12 = 78
Solve for [I]m[/I] in the equation m + 12 + 2m + 12 + 4m + 12 = 78
[SIZE=5][B]Step 1: Group the m terms on the left hand side:[/B][/SIZE]
(1 + 2 + 4)m = 7m
[SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE]
12 + 12 + 12 = 36
[SIZE=5][B]Step 3: Form modified equation[/B][/SIZE]
7m + 36 = + 78
[SIZE=5][B]Step 4: Group constants:[/B][/SIZE]
We need to group our constants 36 and 78. To do that, we subtract 36 from both sides
7m + 36 - 36 = 78 - 36
[SIZE=5][B]Step 5: Cancel 36 on the left side:[/B][/SIZE]
7m = 42
[SIZE=5][B]Step 6: Divide each side of the equation by 7[/B][/SIZE]
7m/7 = 42/7
m = 6
Rick's age = 6 * 4 = [B]24
[URL='https://www.mathcelebrity.com/1unk.php?num=m%2B12%2B2m%2B12%2B4m%2B12%3D78&pl=Solve']Source[/URL]
[/B]

In this class of 4/5 students are right handed. if there are 20 right handed students, what is the t

In this class of 4/5 students are right handed. if there are 20 right handed students, what is the total number of students in this class?
Let x be the total number of students in the class. We have:
4/5x = 20
Cross multiplying or using our [URL='http://www.mathcelebrity.com/1unk.php?num=4x%3D100&pl=Solve']equation calculator[/URL], we get:
4x = 100
Divide each side by 4
[B]x = 25[/B]

Ina school, out of 300 students, 70% are girls and 30% are boys. if 30 girls leave and no new boy is

Ina school, out of 300 students, 70% are girls and 30% are boys. if 30 girls leave and no new boy is admitted, what is the new% of girls in the school.
Current ratios:
[LIST]
[*]Girls = 70% of 300 = 210
[*]Boys = 30% of 300 = 90
[/LIST]
Ratios after girls leave:
[LIST]
[*]Girls = 210 - 30 = 180
[*]Boys = 90
[*]Total = 180 + 90 = 270
[*]Girls Percent = 180/270 = 2/3 = [B]66 & 2/3%[/B]
[/LIST]

Isaac invested $5000 at two different rates, 4% and 6.5% if his total interest income was $250, how

Isaac invested $5000 at two different rates, 4% and 6.5% if his total interest income was $250, how much did he invest at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=5000&i1=4&i2=6.5&itot=250&pl=Calculate']split fund calculator[/URL], we have the following investments per fund:
Fund 1: [B]$3,000[/B]
Fund 2: [B]$2,000[/B]

It takes Spot 2 hours to paint a fence and Steven 4 hours to paint the same fence. If they work toge

It takes Spot 2 hours to paint a fence and Steven 4 hours to paint the same fence. If they work together, how long will it take them to paint the fence?
Spot paints 1/2 of a fence in an hour
Steven paints 1/4 of a fence in an hour
Together, in an hour, they paint 1/2 + 1/4 of a fence in an hour
1/2 = 2/4, so we have 2/4 + 1/4 = 3/4 of a fence in an hour
Meaning they take another 20 minutes to pain the last 1/4 of the fence
[B]1 hour + 20 minutes[/B] is the total time it takes

Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he

Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he have?
Let the number of 5 dollar bills be f. Let the number of 2 dollar bills be t. We're given two equations:
[LIST=1]
[*]f + t = 34
[*]5f + 2t = 116
[/LIST]
We have a system of equations, which we can solve 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answers:
[LIST]
[*][B]f = 16[/B]
[*][B]t = 18[/B]
[/LIST]

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocola

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
If Jack had 2 chocolates left, then the total given to his friends is:
50 - 2 = 48
Let f be the number of friends at his birthday party. Then we have:
3f = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=3f%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 16[/B]

Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 point

Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 points
The phrase [I]total[/I] means a sum, so we have the following equation:
15 + p = 34
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=15%2Bp%3D34&pl=Solve']type this equation into our search engine [/URL]and we get:
p = [B]19[/B]

Jake bought s shirts. they were $7 each. Write an equation to represent the total amount that Jake p

Jake bought s shirts. they were $7 each. Write an equation to represent the total amount that Jake paid for the shirts
Since Amount = Price * Quantity, we have:
[B]7s[/B]

Jan brought 10 vases of 5 roses each. Jow many roses did she buy?

10 Vases * 5 roses in each vase = 50 total roses.

Jane is twice a old as Joel. If their ages total 63, how old is Joel?

Jane is twice a old as Joel. If their ages total 63, how old is Joel?
Joel = j
Jane = 2j
j + 2j = 63
3j = 63
Divide each side by 3:
3j/3 = 63/j
Cancel the 3's on the left side:
j = [B]21[/B]

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. H

Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. How many nickels does Jason have?
Let the number of nickels be n
Let the number of dimes be d
We're given two equations:
[LIST=1]
[*]d = n
[*]0.05n + 0.1d = 2.25
[/LIST]
Substitute equation (1) for d into equation (2):
0.05n + 0.1n = 2.25
Solve for [I]n[/I] in the equation 0.05n + 0.1n = 2.25
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(0.05 + 0.1)n = 0.15n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
0.15n = + 2.25
[SIZE=5][B]Step 3: Divide each side of the equation by 0.15[/B][/SIZE]
0.15n/0.15 = 2.25/0.15
n = [B]15[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.1n%3D2.25&pl=Solve']Source[/URL]

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]

Jay earns S amount per day for working in a company. His total expenses per day is equal to the amou

Jay earns S amount per day for working in a company. His total expenses per day is equal to the amount E. Write an expression to show how much he earned per day in a month. Suppose he is working for 20 days per month.
[LIST=1]
[*]Each day, Jay earns a profit of S - E.
[*]For one month (30 days), he earns 30(S - E)
[*]For 20 working days in a month, he earns 20(S - E)
[/LIST]

Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was cha

Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was charged. A sales tax of 4% was also charged on the ticket price and the handling charges. If the total charge for four tickets was $407.68, what was the ticket price? Round to the nearest dollar.
with a ticket price of t, we have the total cost written as:
1.04 * (7*4 + 4t)= 407.68
Divide each side by 1.04
1.04 * (7*4 + 4t)/1.04= 407.68/1.04
Cancel the 1.04 on the left side and we get:
7*4 + 4t = 392
28 + 4t = 392
To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=28%2B4t%3D392&pl=Solve']type it in our math engine[/URL] and we get:
t = [B]91[/B]

Jayden spent $46.20 on 12 galllons of gasoline. What was the price per gallon?

Jayden spent $46.20 on 12 galllons of gasoline. What was the price per gallon?
Price per gallon = Total spend / number of gallons
Price per gallon = $46.20/12
Price per gallon = $[B]3.85[/B]

Jeni sees 104 octopus legs in the aquarium how many octopuses are there ?

Jeni sees 104 octopus legs in the aquarium how many octopuses are there ?
An octopus has 8 legs. So the total number of octupuses are:
Total octopuses = Total legs / 8
Total octopuses = 104 / 8
Total octopuses = [B]13[/B]

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after wo

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.
Since Jenny makes 9 dollars for each hour of work, then her total pay (p) is her hourly rate times the number of hours worked:
[B]p = 9h[/B]

Jerry’s Bakery makes 144 muffins daily. How many muffins do they make in 7 days? Explain.

Jerry’s Bakery makes 144 muffins daily. How many muffins do they make in 7 days? Explain.
Total muffins = Muffins per day * number of days
Total muffins = 144 * 7
Total muffins = [B]1,008[/B]

Jessica has at most to spend $40 and a pair of pants and shirts. She finds a pair of pants for $12.

Jessica has at most to spend $40 and a pair of pants and shirts. She finds a pair of pants for $12. Shirts cost $4 each. How many shirts can she buy?
[U]Calculate the amount for shirts:[/U]
Amount for shirts = Total Spend - Cost of pants
Amount for shirts = 40 - 12
Amount for shirts = 28
Calculate the amount of t-shirts Jessica can buy:
T-shirts to buy = Amount for shirts / cost per shirt
T-shirts to buy = 28/4
T-shirts to buy = [B]7[/B]

Jessie had 8 apples. Katie had 3 more. How many apples does Katie have

Jessie had 8 apples. Katie had 3 more. How many apples does Katie have
3 more means we add to Jessie's total:
Katie = Jessie + 3
Katie = 8 + 3
Katie = [B]11[/B]

Jessie works in a hat shop for 4 hours per day. She worked a total of 592 hours over the past year.

Jessie works in a hat shop for 4 hours per day. She worked a total of 592 hours over the past year. How many days did she turn up for work?
Days worked = Total Hours Worked / Hours worked per day
Days worked = 592/4
Days worked = [B]148 days[/B]

Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes f

Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes for $34. Jack buys 10 carrots and 7 tomatoes for $29. How much does each carrot and each tomato cost?
Let the cost of carrots be c and the cost of tomatoes be t. Since the total cost is price times quantity, We're given two equations:
[LIST=1]
[*]12c + 8t = 34 <-- Jill
[*]10c + 7t = 29 <-- Jack
[/LIST]
We have a system of equations. We can solve this one of three ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]t = 2[/B]
[*][B]c = 1.5[/B]
[/LIST]

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]

jimmy has 5 apples and beth has 8 apples how many apples do they have together

jimmy has 5 apples and beth has 8 apples how many apples do they have together
[U]The word [I]together[/I] means we add:[/U]
Total Apples = Jimmy's apples + Beth's apples
Total Apples = 5 + 8
Total Apples = [B]13[/B]

Joe buys 9 cds for the same price, he also buys a dvd for 20. His total bill is 119. Find the cost o

Joe buys 9 cds for the same price, he also buys a dvd for 20. His total bill is 119. Find the cost of one cd.
[U]Let c be the cost of one CD. Set up the equation:[/U]
9c + 20 = 119
[U]Use the [URL='http://www.mathcelebrity.com/1unk.php?num=9c%2B20%3D119&pl=Solve']equation solver[/URL]:[/U]
[B]c = 11[/B]

Joe earns $9 per hour. He worked x hours on both Wednesday and Friday, and 8 hours on both Tuesday a

Joe earns $9 per hour. He worked x hours on both Wednesday and Friday, and 8 hours on both Tuesday and Saturday. Write an expression to represent how much joe earned.
Earnings = Hourly Rate * hours worked, so we have:
[LIST]
[*]Wednesday: 9x
[*]Friday: 9x
[*]Tuesday: 9(8) = 72
[*]Saturday: 9(8) = 72
[/LIST]
Joe's total earnings come from adding up all 4 days:
9x + 9x + 72 + 72
Combine like terms:
(9 + 9)x + (72 + 72)
[B]18x + 144[/B]

joe plans to watch 3 movies each month. white an equation to represent the total number of movies n

joe plans to watch 3 movies each month. white an equation to represent the total number of movies n that he will watch in m months
Build movie equation. 3 movies per month at m months means we multiply:
[B]n = 3m[/B]

Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales.

Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales. What was joe’s total sales if he earned $507 last week
Let s be total Sales. 6.5% is 0.065 as a decimal, so Joe's earnings are given by:
0.065s + 325 = 507
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.065s%2B325%3D507&pl=Solve']type this equation into our math engine[/URL] and we get:
s = [B]2800[/B]

Joelle had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil co

Joelle had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?
Subtract the $10 left over from the $24 Joelle started with.
$24 - $10 = $14
Therefore, Joelle spent $14 on seven pencils.
Cost per pencil = Total Pencil Spend / Number of pencils
Cost per pencil = 14 / 7
Cost per pencil = [B]$2[/B]

John delivers 165 newspaper everyday. How many copies of newspaper will he deliver in 30 days

John delivers 165 newspaper everyday. How many copies of newspaper will he deliver in 30 days
Total Newspapers delivered in 30 days = Newspapers delivered per day * 30
Total Newspapers delivered in 30 days = 165 * 30
Total Newspapers delivered in 30 days = [B]4,950[/B]

John has x number of marbles. His friend gave him 6 marbles more. Write an expression for the total

John has x number of marbles. His friend gave him 6 marbles more. Write an expression for the total number of marbles John now has.
More means we add:
[B]x + 6[/B]

John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on

John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on the other. How much did he invest in each if the total amount earned was 880?
The first principal portion is x. Which means the second principal portion is 20,000 - x. We have:
0.04x + 0.05(20,000 - x) = 880
0.04x + 1,000 - 0.05x = 880
Group like terms:
-0.01x + 1000 = 880
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-0.01x%2B1000%3D880&pl=Solve']equation solver[/URL], we get x = [B]12,000[/B]. Which means the other fund has 20,000 - 12,000 = [B]8,000[/B].

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which inequality represents the number of addional games he needs to play in order to score at least 255 points for the season?
Let g be the number of games Jordan plays. Total points per game is 17g. And he’s already scored 153. So we need 17g + 153 to be [I]at least [/I]255. The phrase at least means greater than or equal to, so we use the >= operator for our inequality:
[B]17g + 153 >= 255[/B]

Jose bought 2 movie tickets and a box of popcorn. The popcorn cost $6, and he spent a total of $24.

Jose bought 2 movie tickets and a box of popcorn. The popcorn cost $6, and he spent a total of $24. How much did each ticket cost?
Subtract the cost of the popcorn:
$24 - $6 = $18
2 movie tickets cost $18, so each movie ticket cost $18/2 = [B]$9[/B]

Jose bought a shirt for $25.00. The sales tax was 8%. If Jose paid with $40, what was his change?

Jose bought a shirt for $25.00. The sales tax was 8%. If Jose paid with $40, what was his change?
Total Bill is 25 * 1.08 = $27
Change due = 40 - 27 = $[B]13[/B]

Josh earns $25 per week for cleaning his room. He cleaned his room for 7 weeks. How much money did J

Josh earns $25 per week for cleaning his room. He cleaned his room for 7 weeks. How much money did Josh earn?
Total Earnings = Room cleaning Fee Per Week * Number of Weeks
Total Earnings = $25 * 7
Total Earnings = [B]$175[/B]

Jow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. W

Jow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. What was the cost of one CD?
Let the price of each cd be c. We're given the equation:
9c + 9.45 = 118.89
[URL='https://www.mathcelebrity.com/1unk.php?num=9c%2B9.45%3D118.89&pl=Solve']We type this equation into our search engine[/URL] and we get:
c = [B]12.16[/B]

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Whi

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Which inequality models this situation?
[U]Let d be the number of dimes and q be the number of quarters[/U]
[B]0.1d + 0.25q < 14.75[/B]

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Whi

Juan has d dimes and q quarters in his pocket. The total value of the coins is less than $14.75. Which inequality models this situation?
Since dimes are worth $0.10 and quarters are worth $0.25, we have:
[B]0.10d + 0.25q < 14.75[/B]

juan sells raffle tickets at a charity event for $6 each.How many tickets does he have to sell to ma

juan sells raffle tickets at a charity event for $6 each.How many tickets does he have to sell to make $144?
Tickets needed = Total Sales / Cost per ticket
Tickets needed = 144/6
Tickets needed = [B]24[/B]

Julia has a bucket of water that weighs 10lbs. The total weight is 99% water. She leaves the bucke

Julia has a bucket of water that weighs 10lbs. The total weight is 99% water. She leaves the bucket outside overnight and some of the water evaporates, in the morning the water is only 98% of the total weight. What is the new weight?
Setup the proportion:
0.99/10 = 0.98/w
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=0.99&num2=0.98&den1=10&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]w = 9.899 lbs[/B].

Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total a

Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total amount of money Julio has after x weeks
f(x) = Savings per week * number of weeks + starting amount
f(x) = [B]10x + 150[/B]

Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the nu

Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of Math is Fun she sells. Suppose that x and y are related by the equation 2500+110x=y. What is Kaitlin totalm pay if she doesnt sell any copies of Math is Fun?
We want the value of y when x = 0.
y = 2500 + 110(o)
y = 2500 + 0
[B]y = 2500[/B]

Karen wants to buy new shoes. There is a promotion for 3 pairs of sneakers for $450.75, how much wou

Karen wants to buy new shoes. There is a promotion for 3 pairs of sneakers for $450.75, how much would one pair of sneakers cost?
Cost per sneaker = Total Cost / number of sneakers
Cost per sneaker = 450.75/3
Cost per sneaker = [B]150.25[/B]

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most

Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most She spent on oranges
[U]Assumptions and givens:[/U]
[LIST]
[*]Let a be the total cost of apples
[*]Let o be the total cost of oranges
[/LIST]
The phrase [I]at most[/I] means less than or equal to, so we have:
a + o <= 2.50
[U]Find the cost of apples (a)[/U]
a = price per apple * quantity of apples
a = 0.36 * 5
a = 1.8
Our new inequality with a = 1.8 is:
1.8 + o <= 2.50
[URL='https://www.mathcelebrity.com/1unk.php?num=1.8%2Bo%3C%3D2.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]o <= 0.7[/B]

Keith is going to Renaissance Festival with $120 to pay for his admission, food and the cost of game

Keith is going to Renaissance Festival with $120 to pay for his admission, food and the cost of games. He spends a total of $85 on admission and food. Games cost $5 each. Which inequality models the maximum number of games Keith can play.
Let the number of games be g. Keith can spend less than or equal to 120. So we have
[B]5g + 85 <= 120
[/B]
If we want to solve the inequality for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=5g%2B85%3C%3D120&pl=Solve']type it in our search engine[/URL] and we have:
g <= 7

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]

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a to

Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive?
Let t = number of 20 bills and f = number of 50 bills. We have two equations.
(1) 20t + 50f = 390
(2) t + f = 15
[U]Rearrange (2) into (3) for t, by subtracting f from each side:[/U]
(3) t = 15 - f
[U]Now substitute (3) into (1)[/U]
20(15 - f) + 50f = 390
300 - 20f + 50f = 390
[U]Combine f terms[/U]
300 + 30f = 390
[U]Subtract 300 from each side[/U]
30f = 90
[U]Divide each side by 30[/U]
[B]f = 3[/B]
[U]Substitute f = 3 into (3)[/U]
t = 15 - 3
[B]t = 12[/B]

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The tot

Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type?
Let d be dimes and q be quarters. Set up two equations from our givens:
[LIST=1]
[*]d + q = 41
[*]0.1d + 0.25q = 7.85
[/LIST]
[U]Rearrange (1) by subtracting q from each side:[/U]
(3) d = 41 - q
[U]Now, substitute (3) into (2)[/U]
0.1(41 - q) + 0.25q = 7.85
4.1 - 0.1q + 0.25q = 7.85
[U]Combine q terms[/U]
0.15q + 4.1 = 7.85
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.15q%2B4.1%3D7.85&pl=Solve']equation calculator[/URL], we get:[/U]
[B]q = 25[/B]
[U]Substitute q = 25 into (3)[/U]
d = 41 - 25
[B]d = 16[/B]

Kevin and Randy Muise have a jar containing 52 coins, all of which are either quarters or nickels.

Kevin and Randy Muise have a jar containing 52 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $6.20. How many of each type of coin do they have?
Let q be the number of quarters, and n be the number of nickels. We have:
[LIST=1]
[*]n + q = 52
[*]0.05n + 0.25q = 6.20
[/LIST]
We can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we choose, we get the same answer:
[LIST]
[*][B]n = 34[/B]
[*][B]q = 18[/B]
[/LIST]

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying fo

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying for her marketing class, 12 hours studying for her statistics class, and 8 hours studying for her business law class. What percent of her study time does she spend for her statistics class?
The percentage equals hours spent on statistics divided by total hours spent studying for everything.
[U]Calculate total study hours:[/U]
Total Study Hours = Marketing Class Study Hours + Statistics Class Study Hours + Business Law Study Hours
Total Study Hours = 10 + 8 + 12
Total Study Hours = [B]30[/B]
[U]Calculate Statistics Study Hours Percentage:[/U]
Statistics Study Hours Percentage = Statistics Class Study Hours / Total Study Hours
Statistics Class Study Hours = 8/30
Using our [URL='https://www.mathcelebrity.com/perc.php?num=8&den=30&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']fraction to decimal calculator[/URL], we get
Statistics Class Study Hours = [B]26.67%[/B]

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test
This is a missing average problem.
Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60?
[SIZE=5][B]Setup Average Equation:[/B][/SIZE]
Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers
60 = (68 + 72 + x)/3
[SIZE=5][B]Cross Multiply[/B][/SIZE]
68 + 72 + x = 60 x 3
x + 140 = 180
[SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE]
x + 140 - 140 = 180 - 140
x = [B]40[/B]

Kimi has 62 red peppers and g green peppers. Choose the expression that shows how many peppers Kimi

Kimi has 62 red peppers and g green peppers. Choose the expression that shows how many peppers Kimi has.
We add to get the total peppers:
[B]62 + g[/B]

Larry and his friend split the dinner bill evenly. They each paid $21.34. What was the cost of dinne

Larry and his friend split the dinner bill evenly. They each paid $21.34. What was the cost of dinner?
Total Bill = Larry's portion + Friend's portion
Total Bill = 21.34 + 21.34
Total Bill = [B]$42.68[/B]

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7%

Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate.
Let x be the amount invested at 6%. Then 31000 - x is invested at 7%.
We have the following equation:
0.06x + (31000 - x)0.07 = 2090
Simplify:
0.06x + 2170 - 0.07x = 2090
Combine like Terms
-0.01x + 2170 = 2090
Subtract 2170 from each side
-0.01x = -80
Divide each side by -0.01
x = [B]8000 [/B]at 6%
Which means at 7%, we have:
31000 - 8000 = [B]23,000[/B]

last week, bill drove 252 miles. This week, he drove m miles. Using m , write an expression for the

last week, bill drove 252 miles. This week, he drove m miles. Using m, write an expression for the total number of miles he drove in the two weeks
We add the distance driven:
[B]252 + m[/B]

Last year, Eric had $20,000 to invest. He invested some of it in an account that paid 10% simple int

Last year, Eric had $20,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 7% simple interest per year. After one year, he received a total of $1880 in interest. How much did he invest in each account?
Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=20000&i1=10&i2=7&itot=1880&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]Fund 1 = 16,000[/B]
[*][B]Fund 2 = 4,000[/B]
[/LIST]

Last year, Greg biked 524 miles. This year, he biked m miles. Using m , write an expression for the

Last year, Greg biked 524 miles. This year, he biked m miles. Using m , write an expression for the total number of miles he biked.
We add both years to get our algebraic expression of miles biked:
[B]m + 524[/B]

Last year, Manuel had $10,000 to invest. He invested some of it in an account that paid 7% simple in

Last year, Manuel had $10,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?
The answer is $9,000 and $1,000 found on [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=10000&i1=7&i2=10&itot=730&pl=Calculate']this calculator[/URL].

Last year, Maria biked M miles. This year, she biked 390 miles. Using m , write an expression for th

Last year, Maria biked M miles. This year, she biked 390 miles. Using m , write an expression for the total number of miles she biked.
[U]Calculate Total miles biked[/U]
Total miles biked = Last Year + This year
Total miles biked = [B]m + 390[/B]

Last year, Miguel had $10,000 to invest. He invested some of it in an account that paid 5% simpl

Last year, Miguel had $10,000 to invest. He invested some of it in an account that paid 5% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $800 in interest. How much did he invest in each account?
Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=10000&i1=5&i2=10&itot=800&pl=Calculate']split fund interest calculator[/URL], we get:
[LIST]
[*][B]4,000 in Fund 1 at 5%[/B]
[*][B]6,000 in Fund 2 at 10%[/B]
[/LIST]

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]

Leifs rich uncle decided to give him $1.00 the first day of Christmas and to double the amount each

Leifs rich uncle decided to give him $1.00 the first day of Christmas and to double the amount each subsequent day. How much money (in dollars) does he recieve after all 12 days of Christmas?
Let's look at each day:
[LIST=1]
[*]1
[*]2
[*]4
[*]8
[*]16
[*]32
[*]64
[*]128
[*]256
[*]512
[*]1024
[*]2048
[/LIST]
Total received:
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 = [B]4,095[/B]

Leo and Zach went to lunch at a cafe. They ordered a spinach salad for $6.55, a tuna sandwich for $4

Leo and Zach went to lunch at a cafe. They ordered a spinach salad for $6.55, a tuna sandwich for $4.75, and 2 glasses of lemonade for $0.85 each. The tax was $1.30. They gave the waiter $15.00. How much change should they have received?
Change = Cash - Total Bill - Tax
Change = $15 - ($6.55 + $4.75 + 2($0.85)) - $1.30
Change = $15 - ($6.55 + $4.75 + $1.70) - $1.30
Change = $15 - $13 - $1.30
Change = $15 - $14.30
Change = [B]$0.70 or 70 cents[/B]

license plate with 4 letter combinations and 3 number combinations

license plate with 4 letter combinations and 3 number combinations
There are 26 total letters and 10 digits [0-9].
We have 26 C 4 * 10 C 3.
[URL='http://www.mathcelebrity.com/permutation.php?num=26&den=4&pl=Combinations']26 C 4[/URL] = 14,950
[URL='http://www.mathcelebrity.com/permutation.php?num=10&den=3&pl=Combinations']10 C 3[/URL] = 120
Total license plate combinations:
14,950 * 120 = [B]1,794,000[/B]

Linda takes classes at both Westside Community College and Pinewood Community College. At Westside,

Linda takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Linda is taking a combined total of 18 credit hours at the two schools. Suppose that she is taking w credit hours at Westside. Write an expression for the combined total dollar amount she paid for her class fees.
Let p be the number of credit hours at Pinewood. We have two equations:
[LIST]
[*]98w for Westside
[*]115p at Pinewood
[*]w + p = 18
[*]Total fees: [B]98w + 115p[/B]
[/LIST]

Lindsey took a total of 8 quizzes over the course of 2 weeks. After attending 5 weeks of school this

Lindsey took a total of 8 quizzes over the course of 2 weeks. After attending 5 weeks of school this quarter, how many quizzes will Lindsey have taken in total? Assume the relationship is directly proportional.
Since the relationship is directly proportional, set up a proportion of quizzes to weeks, where q is the number of quizzes Lindsey will take in 5 weeks:
8/2 = q/5
[URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=q&den1=2&den2=5&propsign=%3D&pl=Calculate+missing+proportion+value']We type this proportion into our search engine[/URL], and we get:
[B]q = 20
[/B]
Another way to look at this is, Lindsey takes 8 quizzes over 2 weeks. This means she takes 4 per week since 8/2 = 4.
So if she takes 4 quizzes per week, then in 5 weeks, she takes 4*5 = 20 quizzes.

Lisa has 32 nickels this is one third of her coins how many coins does she have

Lisa has 32 nickels this is one third of her coins how many coins does she have
Let x be the total amount of coins. we have:
32 = x/3
Cross multiply, we get:
[B]x = 96[/B]

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes.

Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes. If the total value of the coins is 2.18, how many of each denomination does she have?
[U]Set up two equations where p is the number of pennies and d is the number of dimes:[/U]
(1) d + p = 47
(2) 0.1d + 0.01p = 2.18
[U]Rearrange (1) into (3) by solving for d[/U]
(3) d = 47 - p
[U]Substitute (3) into (2)[/U]
0.1(47 - p) + 0.01p = 2.18
4.7 - 0.1p + 0.01p = 2.18
[U]Group p terms[/U]
4.7 - 0.09p = 2.18
[U]Add 0.09p to both sides[/U]
0.09p + 2.18 = 4.7
[U]Subtract 2.18 from both sides[/U]
0.09p = 2.52
[U]Divide each side by 0.09[/U]
[B]p = 28[/B]
[U]Now substitute that back into (3)[/U]
d =47 - 28
[B]d = 19[/B]

Lotto Drawing Probability

Free Lotto Drawing Probability Calculator - Given a lotto drawing with a Pick(x) out of (y) total choices, this calculates the probability of winning that lottery picking all (x) correct numbers.

Louis kept money through a hole inn his pocket. He started with 35 cents, lost 20 cents , put in 75

Louis kept money through a hole inn his pocket. He started with 35 cents, lost 20 cents , put in 75 cents , spent 43 cents, lost 16 cents again, and then put in 14 cents. How much change should there be in his pocket?
The phrase [I]put in[/I] mean we add money to the total
The phrases s[I]pent or lost[/I] mean we subtract
35 - 20 + 75 - 43 - 16 + 14 = [B]45 cents[/B]

Lucas has nickels,dimes,and quarters in the ratio 1:3:2. If 10 of Lucas coins are quarters, how many

Lucas has nickels,dimes,and quarters in the ratio 1:3:2. If 10 of Lucas coins are quarters, how many nickels and dimes does Lucas have?
1 + 3 + 2 = 6.
Quarters account for 2/6 which is 1/3 of the total coin count. Let x be the total number of coins. We have:
1/3x = 10
Multiply each side by 3
x = 30
We have the following ratios and totals:
[LIST]
[*]Nickels: 1/6 * 30 = [B]5 nickels[/B]
[*]Dimes: 3/6 * 30 = [B]15 dimes[/B]
[*]Quarters: 2/6 * 30 = [B]10 quarters[/B]
[/LIST]

Lucas is offered either 15% or $21 off his total shopping bill. How much would have to be spent to m

Lucas is offered either 15% or $21 off his total shopping bill. How much would have to be spent to make the 15% option the best one?
Let the total bill be b. We have:
0.15b > 21 <-- Since 15% is 0.15
Using our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=0.15b%3E21&pl=Show+Interval+Notation']inequality calculator[/URL], we get [B]b>140[/B].
So any bill greater than $140 will make the 15% off option the best one, since the discount will be higher than $21.

Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt?

Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt?
Let Dan's debt be d.
Let Luke's debt be l.
We're given two equations:
[LIST=1]
[*]d + l = 72
[*]l = 3d
[/LIST]
Substitute equation (2) for l into equation (1):
d + 3d = 72
Solve for [I]d[/I] in the equation d + 3d = 72
[SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE]
(1 + 3)d = 4d
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
4d = + 72
[SIZE=5][B]Step 3: Divide each side of the equation by 4[/B][/SIZE]
4d/4 = 72/4
d = [B]18[/B]

luke earns $328 in 8 hours. Find luke’s hourly rate

luke earns $328 in 8 hours. Find luke’s hourly rate
luke’s hourly rate = Total Earnings / Hours Worked
luke’s hourly rate 328/8
luke’s hourly rate = [B]$41[/B]

M deck of cards . Each deck has 52 cards . The total number of cards

M deck of cards . Each deck has 52 cards . The total number of cards.
[B]52M[/B]

Marco puts his coins into stacks. Each stack has 10 coins. He makes 17 stacks of quarters. He makes

Marco puts his coins into stacks. Each stack has 10 coins. He makes 17 stacks of quarters. He makes 11 stacks of dimes. He makes 8 stacks of nickels. How much money does Marco have in his stacks of coins?
[U]Value of Quarters:[/U]
Quarter Value = Value per quarter * coins per stack * number of stacks
Quarter Value = 0.25 * 10 * 17
Quarter Value = 42.5
[U]Value of Dimes:[/U]
Dime Value = Value per dime * coins per stack * number of stacks
Dime Value = 0.10 * 10 * 11
Dime Value = 11
[U]Value of Nickels:[/U]
Nickel Value = Value per nickel * coins per stack * number of stacks
Nickel Value = 0.05 * 10 * 8
Nickel Value = 4
[U]Calculate total value of Marco's coin stacks[/U]
Total value of Marco's coin stacks = Quarter Value + Dime Value + Nickel Value
Total value of Marco's coin stacks = 42.5 + 11 + 4
Total value of Marco's coin stacks = [B]57.5[/B]

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of

Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of weeks x and the total number of quizzes y. Write your answer as an equation with y first, followed by an equals sign.
Our total quizzes equal 2 times the number of weeks (x):
[B]y = 2x[/B]

Marcus bought w poster boards for $3 each

The total is $3 * w = 3w

Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How man

Margaret earns 15 an hour at her job. Each week she earns at least 450 and no more than 600. How many hours does Margaret work each week?
Let h be the hours worked
We know that hourly rate * h equals total earnings.
The phrases at least and no more than signify inequalities, so we have:
450 <= 15h <= 600
Divide each entry by 15:
[B]30 <= h <= 40[/B]
This means Margaret works at least 30 hours a week and no more than 40

Maria paid a fee of $75 to the local golf course. For every 18 holes of goals it was $12.50. How muc

Maria paid a fee of $75 to the local golf course. For every 18 holes of goals it was $12.50. How much did Maria pay to play 36 holes of golf
36 holes is 2 * 18 hole rounds.
[U]Maria's total cost for the trip is:[/U]
Maria's Fee = Local Golf Course Fee + 2(18 hole round fee)
Maria's Fee = 75 + 2(12.50)
Maria's Fee = 75 +25
Maria's Fee = [B]$100[/B]

Maria runs each lap in 5 minutes. She will run less than 7 laps today. What are the possible numbers

Maria runs each lap in 5 minutes. She will run less than 7 laps today. What are the possible numbers of minutes she will run today?
Total Time < Laps * minutes per laps
Total Time < 7 * 5
[B]Total Time < 35[/B]

Marina bought 4 notebooks, which cost b dollars each and 3 pens, which cost c dollars each. How much

Marina bought 4 notebooks, which cost b dollars each and 3 pens, which cost c dollars each. How much money did Marina spend?
Cost = Quantity * Price, so we have total spend S of:
S = [B]4b + 3c[/B]

Mario buys 3 postcards during each day of vacation. After 4 days of vacation, how many total post ca

Mario buys 3 postcards during each day of vacation. After 4 days of vacation, how many total post cards will Mario have bought?
3 postcards per day x 4 days of vacation = [B]12 postcards[/B]

Marion Middle School has 600 students. Mike surveys a random sample of 30 students and finds that 7

Marion Middle School has 600 students. Mike surveys a random sample of 30 students and finds that 7 of them play a musical instrument. How many students at the school are likely to play a musical instrument?
Set up a proportion of those that play musical instruments to total students where m is the amount of students in the 600 who play a musical instrument:
7/30 = m/600
[URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=m&den1=30&den2=600&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get:
m = [B]140[/B]

mark has a drawer full of 12 yellow baseball caps and 18 white baseball caps. What is the probabilit

mark has a drawer full of 12 yellow baseball caps and 18 white baseball caps. What is the probability of the next cap he chooses at random will be yellow?
P(yellow) = yellow caps / Total caps
P(yellow) = 12/(12 + 18)
P(yellow) = 12/30
[URL='https://www.mathcelebrity.com/fraction.php?frac1=12.%2F30&frac2=3%2F8&pl=Simplify']Simplifying this fraction,[/URL] we get:
P(yellow) = [B]2/5[/B]

Martin buys b books at £10 each what is the total cost

Martin buys b books at £10 each what is the total cost
Total Cost = Price * Quantity
Total Cost = £10 * b
Total Cost = [B]£10b[/B]

Mary invested $800, part at 9% per annum and the rest at 12% per annum. After 1 year, the total inte

Mary invested $800, part at 9% per annum and the rest at 12% per annum. After 1 year, the total interest earned was $79.50. How much did she invest at each rate?
Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=800&i1=9&i2=12&itot=79.50&pl=Calculate']split fund calculator[/URL], we get:
[LIST]
[*]Fund 1: $550
[*]Fund 2: $250
[/LIST]

Mary spent a total of $291.94 for a party. She spent $200.29 on food, plus an additional $30.55 for

Mary spent a total of $291.94 for a party. She spent $200.29 on food, plus an additional $30.55 for each hour of the party. How long was the party?
First, figure out the remaining cost after food:
291.94 -200.29 = 91.65
91.65 / 30.55 per hour = 3 hours

Mary went bowling on the weekend. Each game cost $2.50, and the shoe rental $2.00. She spent $14.50

Mary went bowling on the weekend. Each game cost $2.50, and the shoe rental $2.00. She spent $14.50 total. How many games did she bowl?
Set up the equation where g is the number of games. We add the shoe rental fee to the cost per games
2.5g + 2 = 14.50
To solve for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5g%2B2%3D14.50&pl=Solve']type this equation into our search engine[/URL] and we get:
g = [B]5[/B]

Math Written Assignment

The truck bed is 80 inches long, 69 inches wide, and 20 inches tall. So the total volume the truck can carry is:
80 x 69 x 20 = 110,400 cubic inches can be carried each time.
Find out how many gallons in a full tank for the 2003 Ford F150.
Then you calculate the amount of miles you can drive on a full trip.

Matthew works 45 hours at $22.10 per hour and 3 hours overtime at double time. Calculate his total e

Matthew works 45 hours at $22.10 per hour and 3 hours overtime at double time. Calculate his total earnings per week.
If Matthew gets 3 hours overtime, then his regular time is 45 - 3 = 42
[U]Calculate regular hours earnings:[/U]
Regular hours earnings = Hourly Rate * Regular hours worked
Regular hours earnings = 22.10 * 42
Regular hours earnings = 928.20
[U]Calculate overtime hours earnings:[/U]
Double time = twice the regular hourly ratre
Overtime hours earnings = Hourly Rate * 2 * Overtime hours worked
Overtime hours earnings = 22.10 * 2 * 3
Overtime hours earnings = 132.60
[U]Calculate total earnings:[/U]
Total earnings = Regular hours earnings + Overtime hours earnings
Total earnings = 928.20 + 132.60
Total earnings = [B]$1,060.80[/B]

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales.

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales. Last year she sold 344000 worth of products. What percent of her total income was her commission?
Calculate Melinda's commission:
344,000 * 0.05 = 17,200
Calculate her total income for the year
Total Income = Base Pay + Commission
Total Income = 17,000 + 17,200
Total Income = 34,200
Calculate the percent of her income which is commission:
Commission Income Percent = 100 * 17,200/34,200
Commission Income Percent = 100 * 0.5029
[B]Commission Income Percent = 50.29%[/B]

Melissa’s flower shop got a shipment of 252 tuilps. She wants to make bouquets of 12 tulips each. Ho

Melissa’s flower shop got a shipment of 252 tuilps. She wants to make bouquets of 12 tulips each. How many bouquets can Melissa make?
Number of bouquets = Total tulips in shipment / tulips per bouquet
Number of bouquets = 252/12
Number of bouquets = [B]21[/B]

Michelle and Natalie both went out to eat at a new restaurant. Michelle’s bill was $22.50, and she l

Michelle and Natalie both went out to eat at a new restaurant. Michelle’s bill was $22.50, and she left a 15% tip. Natalies bill was $24.25, and she left a 10% tip. Whose total bill was the greatest?
[U]Michelles's total bill:[/U]
Total Bill = Pre-Tax Bill * (1 + tax rate)
Since 15% = 0.15, we have:
Total Bill = 22.50 * 1.15
Total Bill = 25.88
[U]Natalie's total bill:[/U]
Total Bill = Pre-Tax Bill * (1 + tax rate)
Since 10% = 0.10, we have:
Total Bill = 24.25 * 1.10
Total Bill = 26.68
[B]Natalie's[/B] total bill was the greatest.

Miguel bought 8 boxes of chocolate. Each box cost 6.36. How much did he spend

Miguel bought 8 boxes of chocolate. Each box cost 6.36. How much did he spend?
Total spend = Number of boxes * cost per box
Total spend = 8 * 6.36
Total spend = [B]$50.88[/B]

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per b

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per book. What is the royalty he receives? Remember to put the $ symbol in your answer. For example, if your answer is 10 dollars, write $10 in the answer box.
[U]Calculate total sales:[/U]
Total Sales = Number of Books * Price per book
Total Sales = 50,000 * $35
Total Sales = $1,750,000
[U]Now calculate Mike's royalties:[/U]
Royalties = Total Sales * Royalty Percent
Royalties = $1,750,000 * 15%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=15&den1=1750000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Royalties[/URL] = [B]$262,500[/B]

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.
Number of movies equals movies per month times the number of months. So we have:
[B]n = 2m[/B]

Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake troy had 1/4 of

Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake (c) that were in total
Let c be the total number of pieces of cake. Let m be the number of pieces Mindy ate. Let t be the number of pieces Troy ate. We have the following given equations:
[LIST]
[*]m + t = 9
[*]m = 3
[*]t = 1/4c
[/LIST]
Combining (2) and (3) into (1), we have:
3 + 1/4c = 9
Subtract 3 from each side:
1/4c = 6
Cross multiply:
[B]c = 24[/B]

monique made 7 more videos than ana. how many videos did monique make if ana made 12 videos?

monique made 7 more videos than ana. how many videos did monique make if ana made 12 videos?
We add 7 to Ana's videos to get Monique's total:
Monique's videos = Ana's videos + 7
Monique's videos = 12 + 7
Monique's videos = [B]19[/B]

Mortgage

Free Mortgage Calculator - Calculates the monthly payment, APY%, total value of payments, principal/interest/balance at a given time as well as an amortization table on a __standard__ or __interest only__ home or car loan with fixed interest rate. Handles amortized loans.

Mr. Smith wants to spend less than $125 at a zoo. A ticket cost $7 he is taking 2 kids with him. Use

Mr. Smith wants to spend less than $125 at a zoo. A ticket cost $7 he is taking 2 kids with him. Use p to represent the other money he can spend there.
2 kids and Mr. Smith = 3 people.
Total Ticket Cost is 3 people * 7 per ticket = 21
If he has 125 to spend, we have the following inequality using less than or equal to (<=) since he can spend up to or less than 125:
p + 21 <= 125
Subtract 21 from each side:
[B]p <= 104[/B]

Mrs. Davis tutored 2.5 hours on Monday night and 1.5 hours on Tuesday night.she earned $72. How much

Mrs. Davis tutored 2.5 hours on Monday night and 1.5 hours on Tuesday night.she earned $72. How much did mrs. Davis earn per hour?
Total hours tutored: 2.5 + 1.5 = 4 hours
Earnings per hour = Earnings/Total hours
Earnings per hour = 72/4
Earning per hour = [B]$18[/B]

Mrs. Mormon bought 2.5 pounds of grapes and paid $4.72. What was the cost per pound of the grapes?

Mrs. Mormon bought 2.5 pounds of grapes and paid $4.72. What was the cost per pound of the grapes?
Cost per pound = Total Cost / pounds
Cost per pound = $4.72 / 2.5
Cost per pound = [B]$1.89[/B]

Mrs. Taylor is making identical costumes for the dancers in the dance club. She uses 126 pink ribbon

Mrs. Taylor is making identical costumes for the dancers in the dance club. She uses 126 pink ribbons and 108 yellow ribbons.
a) What is the maximum possible number of costumes she can make?
b) How many pink and how many yellow ribbons are on each costume?
a), we want the greatest common factor (GCF) of 108 and 126. [URL='https://www.mathcelebrity.com/gcflcm.php?num1=108&num2=126&num3=&pl=GCF+and+LCM']Using our GCF calculator[/URL] we get:
[B]a) 18 costumes
[/B]
b)
Pink Ribbons per costume = Total Pink Ribbons / GCF in question a
Pink Ribbons per costume = 126/18
Pink Ribbons per costume = [B]7[/B]
[B][/B]
Yellow Ribbons per costume = Total Yellow Ribbons / GCF in question a
Yellow Ribbons per costume = 108/18
Yellow Ribbons per costume = [B]6[/B]

nandita earned $224 last month. she earned $28 by selling cards at a craft fair and the rest of the

nandita earned $224 last month. she earned $28 by selling cards at a craft fair and the rest of the money by babysitting. Complete an equation that models the situation and can be used to determine x, the number of dollars nandita earned last month by babysitting.
We know that:
Babysitting + Card Sales = Total earnings
Set up the equation where x is the dollars earned from babysitting:
[B]x + 28 = 224[/B]
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B28%3D224&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]196[/B]

Narda has $250 and Ding has $170. How much money must Narda give to Ding so that each of them will h

Narda has $250 and Ding has $170. How much money must Narda give to Ding so that each of them will have an equal amount of money?
Find the difference of Narda and Ding's money:
Difference = Narda - Ding
Difference = 250 - 170
Difference = 80
Find half the difference:
Half the difference = 80/2
Half the difference = 40
So Narda must give Ding [B]$40[/B] to have equal amounts:
Narda's new total = 250 - 40 = 210
Ding's new total = 1760 + 40 = 210

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in s

Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in size. What is the total area of the field?
Area of each plot is 5x5 = 25 square feet.
Total area = Area per plot * number of plots
Total area = 25 sq ft * 9
Total area = [B]225 sq ft[/B]

Nolan is paid $9 per hour plus a bonus of $55 per week. If Nolan worked n hours during a week, how m

Nolan is paid $9 per hour plus a bonus of $55 per week. If Nolan worked n hours during a week, how much was he paid?
Total Wage = Hourly Wage + Bonus
Hourly wage = Hourly Rate * Hours worked
Bonus = 55
We have:
Total Wage = [B]9n + 55[/B]

Of the 20 boats at the Mariana, 10 were from Massachusetts. What is the probability that a randomly

Of the 20 boats at the Mariana, 10 were from Massachusetts. What is the probability that a randomly selected boat will be from Massachusetts?
P(Boat from Massachusetts) = Number of Massachusetts boats / Total Boats at the Mariana
P(Boat from Massachusetts) = 10/20
[URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F20&frac2=3%2F8&pl=Simplify']Simplifying this fraction, we get[/URL]:
P(Boat from Massachusetts) = [B]1/2[/B]

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]

olivia earns $2 for every cup of lemonade she sells. How many cups of lemonade does olivia need to s

olivia earns $2 for every cup of lemonade she sells. How many cups of lemonade does olivia need to sell in all to earn $16?
Cups needed = Total Revenue / Cost per cup
Cups needed = 16/2
[URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F2&frac2=3%2F8&pl=Simplify']Cups needed [/URL]= [B]$8[/B]

On a Friday evening a pizza shop had orders for 4 pepperoni, 97 vegetable, and 335 cheese pizzas. If

On a Friday evening a pizza shop had orders for 4 pepperoni, 97 vegetable, and 335 cheese pizzas. If the 4 cooks each made an equal number of pizzas, how many pizzas did each cook make?
Total Pizzas Made = 4 pepperoni + 97 vegetable + 335 cheese
Total Pizzas Made = 436
Equal number of pizzas per cook = 436 pizzas / 4 cooks
Equal number of pizzas per cook = [B]109[/B]

On a Math test, 12 students earned an A. This number is exactly 25% of the total number of students

On a Math test, 12 students earned an A. This number is exactly 25% of the total number of students in the class. How many students are in the class?
Let the total number of students be s. Since 25% is 0.25 as a decimal, We have an equation:
0.25s = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%3D12&pl=Solve']Type this equation into our search engine[/URL], and we get:
s = [B]48[/B]

On Monday 208 student went on a trip to the zoo . All 5 buses were filled and 8 student had to trave

On Monday 208 student went on a trip to the zoo . All 5 buses were filled and 8 student had to travel in car . How many student were in each bus?
Calculate the number of students who traveled by bus:
Total bus Students = Total Students - Total Car Students
Total bus Students = 208 - 8
Total bus Students = 200
Figure how the students per bus:
Students per bus = Total Bus Students / Number of Filled Busses
Students per bus = 200/5
Students per bus = [B]40[/B]

On the first day of school each student in the class of 26 will bring 4 writing books and 2 maths bo

On the first day of school each student in the class of 26 will bring 4 writing books and 2 maths books. How many books will they have altogether?
Each student has 4 books plus 2 math books = 6 total books per student
Calculate total books
Total Books = Number of students * books per student
Total Books = 26 * 6
Total Books = [B]156[/B]

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket?
Let the number of child tickets be c
Let the number of senior citizen tickets be s
We're given two equations:
[LIST=1]
[*]10c + 3s = 82
[*]5c + 8s = 67
[/LIST]
We have a system of simultaneous equations. We can solve it using any one of 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]

One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.

One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.
Set up our equation where b is the number of total bagels
72 = b/3
Multiply each side by 3
[B]b = 216[/B]

One thousand people in. room decide to shake hands with every other person in the room. Instead of o

One thousand people in. room decide to shake hands with every other person in the room. Instead of one handshake per couple, each person must shake both of the hands of every person in the room with both his right and his left hand. (Tom will use his right hand to shake Dave's right hand and then Dave's left hand. Tom will then use his left hand to shake Dave's right hand and then Dave's left hand.) How many total handshakes will take place?
1000 people taken 2 at a time:
[URL='https://www.mathcelebrity.com/permutation.php?num=1000&den=2&pl=Combinations']1000C2[/URL] = 499,500
But each group of 2 makes 4 unique handshakes:
499,500 * 4 = [B]1,998,000[/B]

Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each c

Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each class is $13, otherwise it is $18 for each class. After how many classes is the total cost with the fitness pass the same as the total cost without the fitness pass?
Let the number of classes be c.
For the fitness pass plan, we have the total cost of:
13c + 100
For the flat rate plan, we have the total cost of:
18c
The question asks for c when both plans are equal. So we set both costs equal and solve for c:
13c + 100 = 18c
We [URL='https://www.mathcelebrity.com/1unk.php?num=13c%2B100%3D18c&pl=Solve']type this equation into our math engine[/URL] and we get:
c = [B]20[/B]

Out of 53 teachers 36 drink tea 18 drink coffee, 10 drink neither. how many drink both?

Out of 53 teachers 36 drink tea 18 drink coffee, 10 drink neither. how many drink both?
Let T be tea drinkers
Let C be coffee drinkers
Let (T & C) be Tea & Coffee drinkers.
And 53 are total. So we use the Union formula relation:
C U T = C + T - (C & T)
53 = 18 + 36 - (C & T)
C & T = 53 - (Not C & Not T) since we subtract people who don't drink coffee and don't drink tea
C & T = 53 - 10 = 43
C U T = 18 + 36 - 43
C U T = [B]11[/B]

p decreased by 65 is the same as the total of f and 194

p decreased by 65 is the same as the total of f and 194
p decreased by 65
p - 65
The total of f and 194
f + 194
The phrase [I]is the same as[/I] means equal to, so we set the expressions above equal to each other
[B]p - 65 = f + 194[/B]

Pablo is saving money to buy a game. So far he has saved $22, which is one-half of the total cost

Pablo is saving money to buy a game. So far he has saved $22, which is one-half of the total cost of the game. How much does the game cost?
22 is 1/2 of the cost, so multiply 22 * 2 to get the [B]full cost of $44[/B].

Paper sells for 21 cents per pad. What will 5 pads cost?

Total Cost = Cost Per Pad * Number of Pads
Total Cost = 0.21 * 5
Total Cost = [B]$1.05[/B]

Parallel Resistors

Free Parallel Resistors Calculator - Given a set of parallel resistors, this calculates the total resistance in ohms, denoted R_{t}

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]

Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total s

Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total sales in dollars, xx, which can be represented by g(x)=215+0.035x. Owen is paid $242 per week plus 2.5% of his total sales in dollars, xx, which can be represented by f(x)=242+0.025x. Determine the value of xx, in dollars, that will make their weekly pay the same.
Set the pay functions of Owen and Penelope equal to each other:
215+0.035x = 242+0.025x
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=215%2B0.035x%3D242%2B0.025x&pl=Solve']equation calculator[/URL], we get:
[B]x = 2700[/B]

Percentage of Completion

Free Percentage of Completion Calculator - Given a sales price, total costs, and costs per period, this determines the gross profit to date using the percentage of completion method.

Peter plants 560 rows of pineapple plants with 8 plants in each row. How many pineapple plants does

Peter plants 560 rows of pineapple plants with 8 plants in each row. How many pineapple plants does he have?
Calculate total pineapple plants:
Total pineapple plants = Rows * plants per row
Total pineapple plants = 560 * 8
Total pineapple plants = [B]4,480[/B]

Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Sup

Pleasantburg has a population growth model of P(t)=at^2+bt+P0 where P0 is the initial population. Suppose that the future population of Pleasantburg t years after January 1, 2012, is described by the quadratic model P(t)=0.7t^2+6t+15,000. In what month and year will the population reach 19,200?
Set P(t) = 19,200
0.7t^2+6t+15,000 = 19,200
Subtract 19,200 from each side:
0.7t^2+6t+4200 = 0
The Quadratic has irrational roots. So I set up a table below to run through the values. At t = 74, we pass 19,200. Which means we add 74 years to 2012: 2012 + 74 = [B]2086[/B]
t 0.7t^2 6t Add 15000 Total
1 0.7 6 15000 15006.7
2 2.8 12 15000 15014.8
3 6.3 18 15000 15024.3
4 11.2 24 15000 15035.2
5 17.5 30 15000 15047.5
6 25.2 36 15000 15061.2
7 34.3 42 15000 15076.3
8 44.8 48 15000 15092.8
9 56.7 54 15000 15110.7
10 70 60 15000 15130
11 84.7 66 15000 15150.7
12 100.8 72 15000 15172.8
13 118.3 78 15000 15196.3
14 137.2 84 15000 15221.2
15 157.5 90 15000 15247.5
16 179.2 96 15000 15275.2
17 202.3 102 15000 15304.3
18 226.8 108 15000 15334.8
19 252.7 114 15000 15366.7
20 280 120 15000 15400
21 308.7 126 15000 15434.7
22 338.8 132 15000 15470.8
23 370.3 138 15000 15508.3
24 403.2 144 15000 15547.2
25 437.5 150 15000 15587.5
26 473.2 156 15000 15629.2
27 510.3 162 15000 15672.3
28 548.8 168 15000 15716.8
29 588.7 174 15000 15762.7
30 630 180 15000 15810
31 672.7 186 15000 15858.7
32 716.8 192 15000 15908.8
33 762.3 198 15000 15960.3
34 809.2 204 15000 16013.2
35 857.5 210 15000 16067.5
36 907.2 216 15000 16123.2
37 958.3 222 15000 16180.3
38 1010.8 228 15000 16238.8
39 1064.7 234 15000 16298.7
40 1120 240 15000 16360
41 1176.7 246 15000 16422.7
42 1234.8 252 15000 16486.8
43 1294.3 258 15000 16552.3
44 1355.2 264 15000 16619.2
45 1417.5 270 15000 16687.5
46 1481.2 276 15000 16757.2
47 1546.3 282 15000 16828.3
48 1612.8 288 15000 16900.8
49 1680.7 294 15000 16974.7
50 1750 300 15000 17050
51 1820.7 306 15000 17126.7
52 1892.8 312 15000 17204.8
53 1966.3 318 15000 17284.3
54 2041.2 324 15000 17365.2
55 2117.5 330 15000 17447.5
56 2195.2 336 15000 17531.2
57 2274.3 342 15000 17616.3
58 2354.8 348 15000 17702.8
59 2436.7 354 15000 17790.7
60 2520 360 15000 17880
61 2604.7 366 15000 17970.7
62 2690.8 372 15000 18062.8
63 2778.3 378 15000 18156.3
64 2867.2 384 15000 18251.2
65 2957.5 390 15000 18347.5
66 3049.2 396 15000 18445.2
67 3142.3 402 15000 18544.3
68 3236.8 408 15000 18644.8
69 3332.7 414 15000 18746.7
70 3430 420 15000 18850
71 3528.7 426 15000 18954.7
72 3628.8 432 15000 19060.8
73 3730.3 438 15000 19168.3
74 3833.2 444 15000 19277.2

please solve the third word problem

A Web music store offers two versions of a popular song. The size of the standard version is
2.7
megabytes (MB). The size of the high-quality version is
4.7
MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was
4200
MB. How many downloads of the standard version were there?

please solve the third word problem

A Web music store offers two versions of a popular song. The size of the standard version is
2.7
megabytes (MB). The size of the high-quality version is
4.7
MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was
4200
MB. How many downloads of the standard version were there?
Let s be the standard version downloads and h be the high quality downloads. We have two equations:
[LIST=1]
[*]h = 3s
[*]2.7s + 4.7h = 4200
[/LIST]
Substitute (1) into (2)
2.7s + 4.7(3s) = 4200
2.7s + 14.1s = 4200
Combine like terms:
16.8s = 4200
Divide each side by 16.8
[B]s = 250[/B]

Polygons

Free Polygons Calculator - Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Portfolio Rate of Return

Free Portfolio Rate of Return Calculator - Given a portfolio of individual assets with returns and weights, this calculates the total portfolio rate of return.

Positivity Rate

Free Positivity Rate Calculator - This calculator determines the positivity rate using positive tests and total tests

Rachel buys some scarves that cost $10 each and 2 purses that cost $16 each. The cost of Rachel's to

Rachel buys some scarves that cost $10 each and 2 purses that cost $16 each. The cost of Rachel's total purchase is $62. What equation can be used to find n, the number of scarves that Rebecca buys
Scarves Cost + Purses Cost = Total Cost
[U]Calculate Scarves Cost[/U]
Scarves cost = Cost per scarf * number of scarves
Scarves cost = 10n
[U]Calculate Purses Cost[/U]
Purses cost = Cost per purse * number of purses
Purses cost = 16 * 2
Purses cost = 32
Total Cost = 62. Plug in our numbers and values to the Total Cost equation :
10n + 32 = 62
Solve for [I]n[/I] in the equation 10n + 32 = 62
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 32 and 62. To do that, we subtract 32 from both sides
10n + 32 - 32 = 62 - 32
[SIZE=5][B]Step 2: Cancel 32 on the left side:[/B][/SIZE]
10n = 30
[SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE]
10n/10 = 30/10
n = [B]3[/B]

Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every c

Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every copy of Math is Fun he sells. Let p represent his total pay (in dollars), and let c represent the number of copies of Math is Fun he sells. Write an equation relating to . Then use this equation to find his total pay if he sells 22 copies of Math is Fun.
We want a sales function p where c is the number of copies of Math is Fun
p = Price per sale * c + Base Salary
[B]p = 40c + 1900
[/B]
Now, we want to know Total pay if c = 22
p = 40(22) + 1900
p = 880 + 1900
p = [B]2780[/B]

Ratios

Free Ratios Calculator - * Simplifies a ratio of a:b

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.

Rebound Ratio

Free Rebound Ratio Calculator - Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a

Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. You choose a ball at random.
a. What is the probability that you choose a red or even numbered ball?
b. What is the probability you choose a green ball or a ball numbered less than 5?
a. The phrase [I]or[/I] in probability means add. But we need to subtract even reds so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Red and Even balls are {2, 4, 6, 8, 10, 12}
Our probability is:
P(Red or Even) = P(Red) + P(Even) - P(Red and Even)
P(Red or Even) = 13/18 + 9/18 - 6/18
P(Red or Even) = 16/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=16%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]16/18[/B]
[B][/B]
b. The phrase [I]or[/I] in probability means add. But we need to subtract greens less than 5 so we don't double count:
We have 18 total balls, so this is our denonminator for our fractions.
Green and less than 5 does not exist, so we have no intersection
Our probability is:
P(Green or Less Than 5) = P(Green) + P(Less Than 5) - P(Green And Less Than 5)
P(Green or Less Than 5) = 5/18 + 4/18 - 0
P(Green or Less Than 5) = 9/18
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F18&frac2=3%2F8&pl=Simplify']Fraction Simplify Calculator[/URL], we have:
P(Red or Even) = [B]1/2[/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]

Rick earns $8.50 per hour at his mothers house office. He plans on working 12.5 hours this week. How

Rick earns $8.50 per hour at his mothers house office. He plans on working 12.5 hours this week. How much money will rick earn.
Total Earnings = Hourly Rate * Hours Worked
Total Earnings = 8.50 * 12.5
Total Earnings = [B]$106.25[/B]

Rick sold a total of 75 books during the first 22 days of May. If he continues to sell books at the

Rick sold a total of 75 books during the first 22 days of May. If he continues to sell books at the same rate, how many books will he sell during the month of May?
Set up a proportion of days to books where n is the number of books sold in May:
22/31 = 75/n
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=22&num2=75&den1=31&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] and rounding to the next integer, we get:
n = [B]106[/B]

Rita has spent $16 so far on gifts. The additional amount she will spend will be less than $14. What

Rita has spent $16 so far on gifts. The additional amount she will spend will be less than $14. What are the possible total amounts she will spend?
Rita will spend at least another cent on other gifts above the $16 she spent so far, but no more than $14. Also, the problem says less than 14. 16 + 14 is 30, so that is the top end of her spending.
Let's say her remaining spending is s. Set up the inequality for possible spending values.
[B]16 < s < 30[/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]

Robert and Robert go to the movie theater and purchase refreshments for their friends. Robert spend

Robert and Robert go to the movie theater and purchase refreshments for their friends. Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Let d be the cost of each drink, and p be the price of each popcorn bag. We have 2 equations for our system of equations:
[LIST=1]
[*][B]4d + 9p = 65.25[/B]
[*][B]8d + 3p = 51.75[/B]
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+9p+%3D+65.25&term2=8d+%2B+3p+%3D+51.75&pl=Cramers+Method']system of equations calculator[/URL], we get:
[LIST]
[*]d = 4.5
[*][B]p = 5.25 <-- Since the problem asks for the cost of each popcorn bag[/B]
[/LIST]

Robert buys 3 pounds of bananas at $0.50 per pound and 3 pounds of apples at $1.00 per pound. Which

Robert buys 3 pounds of bananas at $0.50 per pound and 3 pounds of apples at $1.00 per pound. Which of the following expressions represents the total cost of the fruit he bought (in dollars)?
Total Cost of Fruit = Bananas in pounds * cost per banana pound + Apples in pounds * cost per apple pound
Total Cost of Fruit = 3($0.50) + 3($1.00)
Total Cost of Fruit = $1.50 + $3.00
Total Cost of Fruit = [B]$4.00[/B]

Robert has 45 dollars. He buys 6 tshirts and has 7 dollars left over. How much did each tshirt cost?

Let x be the price of one t-shirt. Set up an equation:
6 times the number of t-shirts plus 7 dollars left over get him to a total of 45
6x = 45 - 7
6x = 38
Divide each side by 6
[B]x = 6.33[/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

Ronald scored 4 goals in his first soccer game. He then scored the same amount of goals in his next

Ronald scored 4 goals in his first soccer game. He then scored the same amount of goals in his next 3 games. If Ronald has 10 goals total, how many did he score in each game?
For the remaining 3 games, he scored 10 - 4 = 6 goals.
6 goals divided by 3 games = [B]2 goals in each game[/B].

Ruffa received a 20% commission for every item, which she sold for $75 each. If she sold 124 items,

Ruffa received a 20% commission for every item, which she sold for $75 each. If she sold 124 items, how much was her commission?
[U]Calculate commission per item:[/U]
Commission per item = 75 * 20%
Commission per item = 75 * 0.2
Commission per item = 15
[U]Now, calculate total commission for 124 items:[/U]
Commission for 124 items = Commission per item * 124
Commission for 124 items = 15 * 124
Commission for 124 items = [B]1,860[/B]

s dollars saved and she adds d dollars per week for the next twelve weeks

s dollars saved and she adds d dollars per week for the next twelve weeks
Total savings come from adding current savings plus weekly savings:
[B]s + 12d[/B]

Sales Price Variance

Free Sales Price Variance Calculator - Calculates the Sales Price Variance and Total Variance for a group of products

Sales Tax

Free Sales Tax Calculator - Given a sales price and a total bill, this calculates the sales tax amount and sales tax percentage

Sales tax is currently 9.1%. Write an algebraic expression to represent the total amount paid for an

Sales tax is currently 9.1%. Write an algebraic expression to represent the total amount paid for an item that costs d dollars after tax is added to the purchase.
We need to increase the price by 9.1%. Our expression is:
[B]1.091d[/B]

Sales Tax Question

Cost of an item is $55 the total cost is $58.30 what is the sales tax rate and amount of tax ?
[URL='http://www.mathcelebrity.com/tax.php?p=55&tb=58.30&pl=Calculate+Tax']Answer[/URL]

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 has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how

Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how many dimes?
Let d be the number of dimes. Let q be the number of quarters. We're given two equations:
[LIST=1]
[*]0.1d + 0.25q = 2.25
[*]d + q = 12
[/LIST]
We have a simultaneous system of equations. We can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]d = 5[/B]
[*][B]q = 7[/B]
[/LIST]

Sam purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c

Sam purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Sam paid.
Cost Function is:
[B]c = 4n[/B]
Or, using n as a function variable, we write:
c(n) = 4n

Sandy has 10.0 books, Benny has 24.0 books, and Tim has 33.0 books. How many books do they have toge

Sandy has 10.0 books, Benny has 24.0 books, and Tim has 33.0 books. How many books do they have together?
Total Books = Sandy's books + Benny's books + Tim's books
Total Books = 10.0 + 24.0 + 33.0
Total Books = [B]67.0[/B]

Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies.

Sara has a box of candies. In the box there are 8 pink candies, 7 purple candies and 5 blue candies. She takes one candy and records its color. She then puts it back in the box and draws another candy. What is the probability of taking out a pink candy followed by a blue candy?
[B][U]Calculate the total number of candies:[/U][/B]
Total candies = Pink + Purple + Blue
Total candies = 8 + 7 + 5
Total candies = 20
[B][U]Calculate the probability of drawing one pink candy:[/U][/B]
P(Pink) = 8/20
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Pink) = 2/5
[B][U]Calculate the probability of drawing one blue candy:[/U][/B]
P(Blue) = 5/20 <-- [I]20 options since Sara replaced her first draw[/I]
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Blue) = 1/4
The problem asks for the probability of a Pink followed by a Blue. Since each event is independent, we multiply:
P(Pink, Blue) = P(Pink) * P(Blue)
P(Pink, Blue) = 2/5 * 1/4
P(Pink, Blue) = 2/20
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F20&frac2=3%2F8&pl=Simplify']fraction reduction calculator[/URL], we get:
P(Pink, Blue) = [B]1/10 or 10%[/B]

Sarah rolls 2 fair dice and adds the results from each. Work out the probability of getting a total

Sarah rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is a factor of 6.
Factors of 6 are {6, 12}
[URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=6&opdice=1&rolist=+&dby=&ndby=&montect=+']P(Roll a 6)[/URL] = 5/36
[URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=12&opdice=1&rolist=+&dby=&ndby=&montect=+']P(Roll a 12)[/URL] = 1/36
P(Roll a 6 or Roll a 12) = P(Roll a 6) + P(Roll a 12)
P(Roll a 6 or Roll a 12) = 5/36 + 1/36
P(Roll a 6 or Roll a 12) = 6/36
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F36&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we see that:
P(Roll a 6 or Roll a 12) = [B]1/6[/B]

Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 e

Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 each day and is also paid a commission for each sale she makes. One day, Savannah sold 4 computers and was paid a total of $100. Write an equation for the function P(x), representing Savannah's total pay on a day on which she sells x computers.
If base pay is $90 per day, then the total commission Savannah made for selling 4 computers is:
Commission = Total Pay - Base Pay
Commission = 100 - 90
Commission = $10
Assuming the commission for each computer is equal, we need to find the commission per computer:
Commission per computer = Total Commission / Number of Computers Sold
Commission per computer = 10/4
Commission per computer = $2.50
Now, we build the Total pay function P(x):
Total Pay = Base Pay + Commission * Number of Computers sold
[B]P(x) = 90 + 2.5x[/B]

Shanti had 275 red beads and 3 tines as many blue beads as red beads. She used a total of 156 beads

Shanti had 275 red beads and 3 tines as many blue beads as red beads. She used a total of 156 beads to make a bracelet how many beads did she have left?
Calculate Blue Beads:
Blue Beads =3 * Red Beads
Blue Beads = 3(275)
Blue Beads = 825
Subtract off the beads Shanti used for the bracelet:
825 - 156 = [B]669[/B]

She bought 120 sodas for $1.25 each, 30 pizzas for $12.50 each and 120 packs of skittles for $2 ea

She bought 120 sodas for $1.25 each, 30 pizzas for $12.50 each and 120 packs of skittles for $2 each.
Total Cost = Soda Cost + Pizza Cost + Skittle Cost
Cost = Quantity * Price, so we have:
Total Cost = 120 * 1.25 + 20 * 12.50 + 120 * 2
Total Cost = 150 + 250 + 240
Total Cost = $[B]640[/B]

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked bot

She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith?
Assumptions:
[LIST]
[*]Let b be the number of hours Giselle worked as a blacksmith
[*]Let c be the number of hours Giselle worked as a carpenter
[/LIST]
Givens:
[LIST=1]
[*]b + c = 30
[*]25b + 20c = 690
[/LIST]
Rearrange equation (1) to solve for b by subtracting c from each side:
[LIST=1]
[*]b = 30 - c
[*]25b + 20c = 690
[/LIST]
Substitute equation (1) into equation (2) for b
25(30 - c) + 20c = 690
Multiply through:
750 - 25c + 20c = 690
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=750-25c%2B20c%3D690&pl=Solve']type this equation into our search engine[/URL] and we get:
c = [B]12
[/B]
Now, we plug in c = 12 into modified equation (1) to solve for b:
b = 30 - 12
b = [B]18[/B]

Shelby has already taken 31 quizzes during past quarters, and she expects to have 1 quiz during each

Shelby has already taken 31 quizzes during past quarters, and she expects to have 1 quiz during each week of this quarter. After attending 9 weeks of school this quarter, how many quizzes will Shelby have taken in total?
[U]Calculate the latest quiz amounts:[/U]
1 quiz per week * 9 weeks = 9 quizzes.
[U]Now add that to our starting amount of 31 quizzes[/U]
31 + 9 = [B]40 quizzes[/B]

Shen buys a pack of 9 towels for $24.30. Find the unit price in dollars per towel.

Shen buys a pack of 9 towels for $24.30. Find the unit price in dollars per towel.
Unit Price = Total Price/Units
Unit Price = 24.30/9
Unit Price = [B]2.7[/B]

Six friends went out to dinner. Each person ordered the same dinner, which costs $15.85. The friends

Six friends went out to dinner. Each person ordered the same dinner, which costs $15.85. The friends left a combined tip of $14. What was the total of the bill and tip?
When all six friends eat the same meal, we calculate the total meal bill before the tip:
Total meal bill = Cost per Meal * Number of Friends
Total meal bill = 15.85 * 6
Total meal bill = $95.10
Calculate the Total bill and Tip:
Total Bill and Tip = Total Meal Bill + Tip
Total Bill and Tip = $95.10 + $14
Total Bill and Tip = [B]$109.10[/B]

Six Less than the total of three times a number and negative eight

Six Less than the total of three times a number and negative eight.
Let's take this in pieces:
Three times a number = 3x
The total of this and negative eight means we subtract eight
3x - 8
Six Less than this total means we subtract 6
3x - 8 - 6
Simplify by combining like terms:
[B]3x - 14[/B]

Some History teachers at Richmond High School are purchasing tickets for students and their adult ch

Some History teachers at Richmond High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yang bought 30 student tickets and 30 adult tickets, which cost a total of $750. Mr. Alexander spent $682, getting 28 student tickets and 27 adult tickets. What is the price for each type of ticket?
Let the number of adult tickets be a
Let the number of student tickets be s
We're given two equations:
[LIST=1]
[*]30a + 30s = 750
[*]27a + 28s = 682
[/LIST]
To solve the simultaneous equations, we can use any of three methods below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we use, we get the same answers:
[LIST]
[*][B]a = 18[/B]
[*][B]s = 7[/B]
[/LIST]

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large redwood tree was, the ranger said that he wouldn't tell its height, but would give Sonia a clue. How tall is the redwood tree Sonia asked about?
Sonia said the tree is 64 times my height. The tree is also 112 feet taller than the tree next to it. The two trees plus my height total 597.5 feet.
[LIST]
[*]Rangers's height = n
[*]Tree height = 64n
[*]Smaller tree height = 64n - 112
[*]Total height = 64n - 112 + 64n = 597.5
[/LIST]
Solve for [I]n[/I] in the equation 64n - 112 + 64n = 597.5
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(64 + 64)n = 128n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
128n - 112 = + 597.5
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -112 and 597.5. To do that, we add 112 to both sides
128n - 112 + 112 = 597.5 + 112
[SIZE=5][B]Step 4: Cancel 112 on the left side:[/B][/SIZE]
128n = 709.5
[SIZE=5][B]Step 5: Divide each side of the equation by 128[/B][/SIZE]
128n/128 = 709.5/128
n = 5.54296875
Tree height = 64 * ranger height
Tree height = 64 * 5.54296875
Tree height = [B]354.75 feet[/B]

Split Fund Interest

Free Split Fund Interest Calculator - Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.

Stanley earns $1160 a month. He spends $540 every month and saves the rest. How much will he save in

Stanley earns $1160 a month. He spends $540 every month and saves the rest. How much will he save in 4 years?
[U]Calculate savings amount per month:[/U]
Savings amount per month = Earnings - Spend
Savings amount per month = 1160 - 540
Savings amount per month = 620
[U]Convert years to months[/U]
4 years = 12 * 4 months
4 years = 48 months
[U]Calculate total savings:[/U]
Total Savings = Savings per month * number of months saved
Total Savings = 620 * 48
Total Savings = [B]$29,760
[MEDIA=youtube]sbzRra8dSFs[/MEDIA][/B]

Stephanie and her sister go bowling every weekend and have been keeping track of their wins for the

Stephanie and her sister go bowling every weekend and have been keeping track of their wins for the last couple months. So far, Stephanie has won 8 out the total 18 games that they have played. if Stephanie wishes to have an 80% winning record, how many games in a row will Stephanie have to win, without losing?
Track each game the percentage
[LIST=1]
[*]8 out of 18 = 44.44%
[*]9 out of 19 = 47.37%
[*]10 out of 20 = 50%
[*]11 out of 21 = 52.38%
[*]12 out of 22 = 54.55%
[*]13 out of 23 = 56.52%
[*]14 out of 24 = 58.33%
[*]15 out of 25 = 60%
[*]16 out of 26 = 61.54%
[*]17 out of 27 = 62.96%
[*]18 out of 28 = 64.29%
[*]19 out of 29 = 65.52%
[*]20 out of 30 = 66.67%
[*]21 out of 31 = 67.74%
[*]22 out of 32 = 68.75%
[*]23 out of 33 = 69.7%
[*]24 out of 34 = 70.59%
[*]25 out of 35 = 71.43%
[*]26 out of 36 = 72.22%
[*]27 out of 37 = 72.97%
[*]28 out of 38 = 73.68%
[*]29 out of 39 = 74.36%
[*]30 out of 40 = 75%
[*]31 out of 41 = 75.61%
[*]32 out of 42 = 76.19%
[*]33 out of 43 = 76.74%
[*]34 out of 44 = 77.27%
[*]35 out of 45 = 77.78%
[*]36 out of 46 = 78.26%
[*]37 out of 47 = 78.72%
[*]38 out of 48 = 79.17%
[*]39 out of 49 = 79.59%
[*][B]40 out of 50 = 80%[/B]
[/LIST]
[B]So our answer is 32 games in a row[/B]

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how m

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how many months will I spend a total of $165?
[U]Let the number of months be m. We have a total spend T of:[/U]
cost per month * m + one-time membership fee = T
[U]Plugging in our numbers, we get:[/U]
14m + 25 = 165
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=14m%2B25%3D165&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]10[/B]

Suppose 5% of a package of balloons are yellow balloons. Then what percentage of balloons are a diff

Suppose 5% of a package of balloons are yellow balloons. Then what percentage of balloons are a different color than yellow?
Our total possibilities of any color balloon is 100%. So we have:
Non-yellow balloons = 100% - yellow balloons percent
Non-yellow balloons = 100% - 5%
Non-yellow balloons = [B]95%[/B]

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin doe

Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin does she have?
Set up two equations where d is the number of dimes and q is the number of quarters:
(1) d + q = 10
(2) 0.1d + 0.25q = 1.45
Rearrange (1) into (3) to solve for d
(3) d = 10 - q
Now plug (3) into (2)
0.1(10 - q) + 0.25q = 1.45
Multiply through:
1 - 0.1q + 0.25q = 1.45
Combine q terms
0.15q + 1 = 1.45
Subtract 1 from each side
0.15q = 0.45
Divide each side by 0.15
[B]q = 3[/B]
Plug our q = 3 value into (3)
d = 10 - 3
[B]d = 7[/B]

Suppose two number cubes are rolled. What is the probability of rolling a sum greater than 8?

List out the sums greater than 8:
(4, 5)
(4, 6)
(5, 5)
(5, 6)
(6, 6)
(5, 4)
(6, 4)
(6, 5)
Since there are 6 * 6 = 36 total outcomes, we have the probability of the sum greater than 8 as:
8/36 = 2/9

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a c

Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a combined total of 104 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Let t be the number of hours for math tutoring and w be the number of hours for waitressing. We're given:
[LIST=1]
[*]t + w = 104
[*]14t + 13w = D <-- Combined total dollar amount
[/LIST]

Susie bought 15 pairs of shoes last year for an avarage of 30$ per pair. She sold each pair for 1/3

Susie bought 15 pairs of shoes last year for an avarage of 30$ per pair. She sold each pair for 1/3 of the avagrage price at a consignment shop. How much money did she make at the consigment shop?
Calculate average price:
1/3 the average price is $30/3 = $10
Total money made:
Pairs of Shoes * Average Price
15 * 10 = [B]$150[/B]

Tamira and her 3 friends spent a total of $37 for a large pizza and 4 sodas. Each soda cost $2. Whic

Tamira and her 3 friends spent a total of $37 for a large pizza and 4 sodas. Each soda cost $2. Which equation can be used to find p, the cost of the pizza?
We add the cost of the pizza (p) to the 4 sodas @ $2 each to get 37
p + 4(2) = 37
[B]p + 8 = 37 (This is the equation)
[/B]
If the problem asks you to solve for p, then we [URL='https://www.mathcelebrity.com/1unk.php?num=p%2B8%3D37&pl=Solve']type the equation above into our search engine[/URL] and we get:
p = [B]29[/B]

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total
We have a commission equation below:
Sales * Commission percent = Salary
We're given 4% commission percent and 55,000 salary. With 4% as 0.04, we have:
Sales * 0.04 = 55,000
Divide each side of the equation by 0.04, and we get:
Sales = [B]1,375,000[/B]

Temperature Change

Free Temperature Change Calculator - This calculator determines the total temperature change

Terry recorded the temperature every hour from 8 AM to 1 PM. The temperature at 8 AM was 19?. The te

Terry recorded the temperature every hour from 8 AM to 1 PM. The temperature at 8 AM was 19?. The temperature dropped 4? every hour. What was the temperature at 1 PM? Group of answer choices 1 degree
Set up our temperature function T(h) where h is the number of hours since 8 AM:
T(h) = 19 - 4h <-- We subtract 4h since each hour, the temperature drops 4 degrees
The questions asks for the temperature at 1PM. We need to figure out how many hours pass since 8 AM:
8 AM to 12 PM is 4 hours
12 PM to 1 PM is 1 hour
Total time is 5 hours
So we want T(5):
T(5) = 19 - 4(5)
T(5) = 19 - 20
T(5) = [B]-1?[/B]

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 32

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 327 people entered the park , and the admission fee collected totaled 978.00 dollars . How many children and how many adults were admitted?
Let the number of children's tickets be c. Let the number of adult tickets be a. We're given two equations:
[LIST=1]
[*]a + c = 327
[*]4a + 1.50c = 978
[/LIST]
We can solve this system of equation 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answers:
[LIST]
[*][B]a = 195[/B]
[*][B]c = 132[/B]
[/LIST]

The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day,

The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 281 people entered the park, and the admission fees collected totaled $784 . How many children and how many adults were admitted?
Let c be the number of children and a be the number of adults. We have two equations:
[LIST=1]
[*]a + c = 281
[*]4a + 1.5c = 784
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a%2Bc%3D281&term2=4a+%2B+1.5c+%3D+784&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[LIST]
[*][B]a = 145[/B]
[*][B]c = 136[/B]
[/LIST]

The auto repair shop took 2.5 hours to repair Victoria’s car. The cost of parts was $93, and the tot

The auto repair shop took 2.5 hours to repair Victoria’s car. The cost of parts was $93, and the total bill was $248. What is the shops charge per hour.
Calculate Labor Cost:
Labor Cost = Total bill - Parts
Labor Cost = $248 - $93
Labor Cost = $155
Calculate labor hourly rate:
Labor Hourly Rate = Labor Cost / Number of Labor Hours
Labor Hourly Rate = 155/2.5
Labor Hourly Rate = [B]$62[/B]

The average age of 15 men is 25 years. What is their total age in years?

The average age of 15 men is 25 years. What is their total age in years?
Average Age = Total Ages/Total Men
25 = Total Ages / 15
Cross multiply and we get:
Total Ages = 15 * 25
Total Ages = [B]375[/B]

The cafe needs 170 onions. there are 3 onions in each bag. How many bags should the cafe buy?

The cafe needs 170 onions. there are 3 onions in each bag. How many bags should the cafe buy?
Bags needed = Total Onions / Onions per bag
Bags needed = 170/3
Bags needed = 56.67 ~ [B]57 bags[/B]

The chance of a soldier being an enemy spy is .0005. Out of 10,000 soldiers, how many of them are ex

The chance of a soldier being an enemy spy is .0005. Out of 10,000 soldiers, how many of them are expected to be spies?
Expected Spies = Probability of being a spy * Total Soldiers
Expected Spies = 0.0005 * 10000
Expected Spies = [B]5[/B]

The coach writes the batting order on a piece of paper. How many different ways could the list be wr

The coach writes the batting order on a piece of paper. How many different ways could the list be written?
We have 9 people in a line up. The total lineups are shown by:
9 * 8 * 7 * ... * 2 * 1
Or, 9!. [URL='https://www.mathcelebrity.com/factorial.php?num=9!&pl=Calculate+factorial']Typing 9! in our search engine[/URL] and we get [B]362,880[/B]

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the total cost to park for 5 hours?
Set up our equation where C is cost and h is the number of hours used to park
C = 1.5h + 2.25
With h = 5, we have:
C = 1.5(5) + 2.25
C = 7.5 + 2.25
C = 9.75

The cost of $9 movie tickets for you and three friends

The cost of $9 movie tickets for you and three friends
You and three friends is 4 people.
Cost per Person = Total Cost / Total People
Cost per Person = $9/4
Cost per Person = [B]$2.25[/B]

the cost of d drinks at $2 each and 5 pies at $n each

the cost of d drinks at $2 each and 5 pies at $n each
Total cost = Price * Quantity:
Total cost = [B]2d + 5n[/B]

The cost of having a plumber spend h hours at

The cost of having a plumber spend h hours at your house if the plumber charges $60 for coming to the house and $70 per hour labor:
We have a fixed cost of $60 plus the variable cost of $70h. We add both for our total cost C(h):
[B]C(h) = $70h + 60[/B]

The cost of hiring a car for a day is $60 plus 0.25 cents per kilometer. Michelle travels 750 kilome

The cost of hiring a car for a day is $60 plus 0.25 cents per kilometer. Michelle travels 750 kilometers. What is her total cost
Set up the cost function C(k) where k is the number of kilometers traveled:
C(k) = 60 + 0.25k
The problem asks for C(750)
C(750) = 60 + 0.25(750)
C(750) = 60 + 187.5
C(750) = [B]247.5[/B]

The cost of purchasing a hockey stick and puck if the stick costs 6 less than twice the cost of the

The cost of purchasing a hockey stick and puck if the stick costs 6 less than twice the cost of the puck.
Let the hockey stick cost h, and puck cost p.
Twice the cost of the puck means we multiply p by 2:
2p
6 less than this means we subtract 6:
h = 2p - 6
[B][/B]
The total cost of the hockey stick and puck is:
p + 2p - 6
[B]3p - 6[/B]

The cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. Ho

The cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. How long can a person have the rototiller if the cost must be less than $95?
Setup the inequality:
$19.50 + $7.95x < $95
Subtract 19.50 from both sides:
7.95x < 75.50
Divide each side of the inequality by 7.95 to isolate x
x < 9.5
The next lowest integer is 9. So we take 9 + the first hour of renting to get [B]10 total hours[/B].
Check our work:
$7.95 * 9.5 + $19.50
$71.55 + $19.50 = $91.05

The cost of X pounds of cheese or $6.75 a pound

The cost of X pounds of cheese or $6.75 a pound
Total Cost = Unit Cost * units
Total Cost = [B]$6.75 * x[/B]

The cost to rent a boat is $10. There is also charge of $2 for each person. Which expresion represen

The cost to rent a boat is $10. There is also charge of $2 for each person. Which expresion represents the total cost to rent a boat for p persons?
The cost function includes a fixed cost of $10 plus a variable cost of 2 persons for p persons:
[B]C(p) = 2p + 10[/B]

The difference between the square of b and the total of b and 9

The difference between the square of b and the total of b and 9
The square of b means we raise b to the power of 2:
b^2
The total of b and 9 means we add 9 to b:
b + 9
The difference means we subtract:
[B]b^2 - (b + 9)[/B]

The difference between the square of b and the total of d and g

The difference between the square of b and the total of d and g
Square of b means we raise b to the 2nd power:
b^2
Total of d and g:
d + g
The difference between the square of b and the total of d and g
[B]b^2 - (d + g)[/B]

The famous Concorde jet travelled at a speed of 2000km/h for two and a half hours. Do you think it c

The famous Concorde jet travelled at a speed of 2000km/h for two and a half hours. Do you think it could make it to its destination which is 5500km away on time
Calculate the total distance traveled @ 2000km/h for 2.5 hours:
d = rt
d = 2000 * 2.5
d = 5,000 km
The answer is [B]no, it cannot make the destination[/B].

The girl’s hockey team won 6 games, lost 3 games, and tied 2 games. What fraction of games did they

The girl’s hockey team won 6 games, lost 3 games, and tied 2 games. What fraction of games did they win?
Win Fraction = Won Games / Total Games Played
Win Fraction = 6 / (6 + 3 + 2)
Win Fraction = [B]6/11[/B]

The Henson family cleaned out all their drawers. They found 47 black pens and 39 blue pens. They als

The Henson family cleaned out all their drawers. They found 47 black pens and 39 blue pens. They also found 6 pens in other colors. How many pens did they find in all?
The phrase [I]in all[/I] means we add, so we have:
Total pens = Black Pens + Blue Pens + Other color pens
Total pens = 47 + 39 + 6
Total pens = [B]92[/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 Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39

The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39 baskets total, how many of each basket did they make?
Let x = 2 point baskets and y = 3 point baskets. We have the following given equations:
[LIST=1]
[*]x + y = 39
[*]2x + 3y = 81
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x%2By%3D39&term2=2x+%2B+3y+%3D+81&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[B]x = 36 <-- 2 point baskets
y = 3 <-- 3[B] point baskets
[/B][/B]
To confirm our work:
[LIST=1]
[*]36 + 3 = 39
[*]2(36) + 3(3) = 72 + 9 = 81
[/LIST]

The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazi

The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazines will the library be able to buy?
Let number of magazines be m. We know that:
Cost per magazine * m = Total Cost
We're given Total Cost = 8040 and Cost per magazine = 3, so we have
3m = 8040
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%3D8040&pl=Solve']type it in our math engine[/URL] and we get:
m = [B]2680[/B]

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a l

The letters that form the word ALGEBRA are placed in a bowl. What is the probability of choosing a letter that is not “A”?
ALGEBRA has 7 letters
Of the 7 letters, we have 2 A's.
So we have 7 - 2 = 5 letters which are not A
P(Not A) = Letters not A / Total letters
P(Not A) = [B]5/7[/B]

The library received 1,125 new books. 45 books fit on each shelf. How many shelves are needed for th

The library received 1,125 new books. 45 books fit on each shelf. How many shelves are needed for the new books?
Shelves needed = Total Books / Number of Shelves
Shelves needed = 1,125/45
Shelves needed = [B]25[/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 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 mean height of a class of 20 children is 1.27 the mean height of 12 boys in the class is 1.29 wh

The mean height of a class of 20 children is 1.27 the mean height of 12 boys in the class is 1.29 what is the mean height of the girls in the class?
The mean of sums is the sum of means. So we have:
Total Height / 20 = 1.27
Cross multiplying, we get:
Total Height = 20 * 1.27
Total Height = 25.4
Boys Height / 12 = 1.29
Cross multiplying, we get:
Boys Height = 12 * 1.29
Boys Height = 15.48
The Problem asks for mean height for girls. The formula is:
Girls Height / # of Girls = Mean of Girls Height
# of Girls = Total children - # of boys
# of Girls = 20 - 12
# of Girls = 8
Girls Height = Total Height - Boys Height
Girls Height = 25.4 - 15.48
Girls Height = 9.92
Plugging this into the Mean of girls height, we get:
9.92 /8 = [B]1.24[/B]

The Oakdale High School Speech and Debate Club hosted its annual car wash fundraiser. Each club memb

The Oakdale High School Speech and Debate Club hosted its annual car wash fundraiser. Each club member brought a bottle of car wash soap, so there were 8 total bottles. 6 of the bottles contained orange soap. If a club member randomly selects 5 bottles to pour into the first soap bucket, what is the probability that all of them contain orange soap?
This is assumed to be draw without replacement, so we have:
[LIST=1]
[*]Draw 1: 6/8
[*]Draw 2: 5/7
[*]Draw 3: 4/6
[*]Draw 4: 3/5
[*]Draw 5: 2/4
[/LIST]
Since they are independent events, we multiply:
6/8 * 5/7 * 4/6 * 3/5 * 2/4
(6 * 5 * 4 * 3 * 2)/(8 * 7 * 6 * 5 * 4)
720/6720
[B]0.1071[/B]

The Palafoxes make $3,840 a month. They spend $1,600 for rent. What fraction of their income goes to

The Palafoxes make $3,840 a month. They spend $1,600 for rent. What fraction of their income goes to rent?
Rent Payment Fraction = Rent Payment / Total Income
Rent Payment Fraction = 1600 / 3840
Our greatest common factor of 1600 and 3840 is 320.
So if we divide 1600 and 3840 by 320, we get:
Rent Payment Fraction = [B]5/12
[MEDIA=youtube]DsXk6AKT18M[/MEDIA][/B]

The pieces of a 500 piece puzzle are stored in three containers. 220 pieces are in the first contain

The pieces of a 500 piece puzzle are stored in three containers. 220 pieces are in the first container and 180 pieces are in the second container. What percentage of the pieces is in the third container?
[U]Calculate the number of pieces in the 3rd container:[/U]
Pieces in container 3 = Total Puzzle Pieces - Pieces in container 2 - Pieces in container 1
Pieces in container 3 = 500 - 220 - 180
Pieces in container 3 = 100
Calculate the percentage of pieces in the 3rd container:
Percentage of pieces in container 3 = 100% * Pieces in container 3 / Total puzzle pieces
Percentage of pieces in container 3 = 100% * 100 / 500
Percentage of pieces in container 3 = 100% * 0.2
Percentage of pieces in container 3 = [B]20%[/B]

THE PLAYER CHOSE 20 OUT OF 70 NUMBERS IN A GAME OF CHANCE. ...WHEN THE SHOW BEGIN,THE BANKER WILL

THE PLAYER CHOSE 20 OUT OF 70 NUMBERS IN A GAME OF CHANCE. ...WHEN THE SHOW BEGIN,THE BANKER WILL THEN RAFFLE OR DO A DRAW WHERE IN THE BANKER PICKS AS WELL 20 OUT OF 70 NUMBERS. .....NOW HERES THE TRICK, FOR YOU TO BEAT THE BANKER .YOUR CHOSEN 20 NUMBERS SHOULD NOT MATCH ANY OF THE BANKER 20 0UT OF 70 NUMBERS THAT HAD BEEN DRAWS IN THE GAME OF SHOW. IF THE 20 NUMBERS YOU HAVE ARE TOTALLY DIFFERENT FROM THE BANKERS 20 NUMBERS DRAWN THEN YOU WIN THE PRICE.
Banker Draw Numbers not matching Total numbers Probability Probability Decimal Cumulative Probability
1 50 70 50/70 0.7142857143 0.7142857143
2 49 69 49/69 0.7101449275 0.5072463768
3 48 68 48/68 0.7058823529 0.358056266
4 47 67 47/67 0.7014925373 0.2511737985
5 46 66 46/66 0.696969697 0.1750605262
6 45 65 45/65 0.6923076923 0.1211957489
7 44 64 44/64 0.6875 0.0833220774
8 43 63 43/63 0.6825396825 0.05687062425
9 42 62 42/62 0.6774193548 0.03852526159
10 41 61 41/61 0.6721311475 0.02589402828
11 40 60 40/60 0.6666666667 0.01726268552
12 39 59 39/59 0.6610169492 0.01141092772
13 38 58 38/58 0.6551724138 0.007476125057
14 37 57 37/57 0.649122807 0.004852923282
15 36 56 36/56 0.6428571429 0.003119736396
16 35 55 35/55 0.6363636364 0.001985286797
17 34 54 34/54 0.6296296296 0.001249995391
18 33 53 33/53 0.6226415094 0.000778299017
19 32 52 32/52 0.6153846154 0.0004789532412
20 31 51 31/51 0.6078431373 [B]0.0002911284407 [/B]

The population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what w

The population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what was the population in 1981?
Calculate the difference in years:
Difference = 1981 - 1945
Difference = 36
Calculate doubling periods:
Doubling periods = Total years / Doubling time
Doubling periods = 36/12
Doubling periods = 3
Population = Initial Population * 2^doubling periods
Population = 11005 * 2^3
Population = 11005 * 8
Population = [B]88,040[/B]

The price of a cheap backpack is $15 less than an expensive backpack. When Emily bought both, she pa

The price of a cheap backpack is $15 less than an expensive backpack. When Emily bought both, she paid $75. What is the cost of the cheap backpack?
backpack cost = b
Cheap backpack = b - 15
The total of both items equals 75:
b + b - 15 = 75
Solve for [I]b[/I] in the equation b + b - 15 = 75
[SIZE=5][B]Step 1: Group the b terms on the left hand side:[/B][/SIZE]
(1 + 1)b = 2b
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2b - 15 = + 75
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -15 and 75. To do that, we add 15 to both sides
2b - 15 + 15 = 75 + 15
[SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE]
2b = 90
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2b/2 = 90/2
b = 45
Cheap backpack = 45 - 15 = [B]30
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2Bb-15%3D75&pl=Solve']Source[/URL][/B]

the quotient of 7 and the total of 5 and x

the quotient of 7 and the total of 5 and x
The total of 5 and x
5 + x
the quotient of 7 and the total of 5 and x
[B]7/(5 + x)[/B]

The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day

The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each senior citizen ticket and each child ticket?
Let the cost of child tickets be c
Let the cost of senior tickets be s
Since revenue = cost * quantity, we're given two equations:
[LIST=1]
[*]9c + 3s = 75
[*]5c + 8s = 67
[/LIST]
To solve this simultaneous group of equations, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]

The ratio of adults to children at the beach is 4:3. If there are a total of 56 people how many are

The ratio of adults to children at the beach is 4:3. If there are a total of 56 people how many are adults? How many are children?
Using our [URL='http://www.mathcelebrity.com/ratio.php?simpratio=100%3A350&rs=4%3A3&rtot=56&pl=Calculate+Ratio']ratio calculator[/URL], we get:
[LIST]
[*][B]32 adults[/B]
[*][B]24 children[/B]
[/LIST]

The ratio of men to women working for a company is 5 to 3 . If there are 75 men working for the

The ratio of men to women working for a company is 5 to 3 . If there are 75 men working for the company, what is the total number of employees?
We read this as a proportion, of men to women.
5/3 = 75/w where w is the number of women for 75 men.
Entering this expression into our [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=75&propsign=%3D&den1=3&den2=w&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]w = 45[/B].

The ratio of men to women working for a company is 3 to 4. If there are 81 men working for the compa

The ratio of men to women working for a company is 3 to 4. If there are 81 men working for the company, what is the total number of employees?
Men to women is 3:4. Set up a proportion where w is the number of women:
3/4 = 81/w
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=81&den1=4&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get w = 108.
The problem asks for total employees, so we add men and women:
Total Employees = Men + Women
Total Employees = 81 + 108
Total Employees = [B]189[/B]

The ratio of men to women working for a company is 4 to 7. If there are 319 employees total, how man

The ratio of men to women working for a company is 4 to 7. If there are 319 employees total, how many men work for the company?
[B]116[/B] using our [URL='http://www.mathcelebrity.com/ratio.php?simpratio=100%3A350&rs=4%3A7&rtot=319&pl=Calculate+Ratio']ratio calculator[/URL]

The ratio of the number of carabaos, goats, and cows in a farm is 5:1:2. If there are 48 animals of

The ratio of the number of carabaos, goats, and cows in a farm is 5:1:2. If there are 48 animals of these kinds in his backyard how many of them are goats
Calculate total ratio:
5 + 1 + 2 = 8
Multiply fractional portion of goats by total animals in the backyard.
1/8 * 48 = [B]6 goats[/B]

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk con

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk [I]m[/I] and cups of juice [I]j[/I] a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?
Total calcium = Milk calcium + Juice Calcium
Calculate Milk Calcium:
Milk Calcium = 299m where m is the number of cups of milk
Calculate Juice Calcium:
Juice Calcium = 261j where j is the number of cups of juice
The phrase [I]meet or exceed[/I] means greater than or equal to, so we have an inequality, where Total Calcium is greater than or equal to 1000. So we write our inequality as:
Milk calcium + Juice Calcium >= Total Calcium
[B]299m + 261j >= 1000[/B]

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5. If there were 4570 no votes, what was the total number of votes?
Set up a proportion where y is the number of yes votes to 4570 no votes
6/5 = y/4570
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=6&num2=y&den1=5&den2=4570&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
[B]y = 5484[/B]

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 4 to 3 . If there were 2958 no votes, what was the total number of votes?
Set up a ratio of yes to no votes
4/3 = x/2958
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=x&den1=3&den2=2958&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get x = 3,944 for yes votes.
Adding yes votes and no votes together to get total votes, we get:
Total Votes = Yes Votes + No Votes
Total Votes = 3,944 + 2,958
Total Votes = [B]6,902[/B]

The sales price s of a pair of shoes plus 4% sales tax

The sales price s of a pair of shoes plus 4% sales tax
Total price is s(1 + 0.04) or [B]s(1.04)[/B]

The sales tax rate in a city is 7.27%. How much sales tax is charged on a purchase of 5 headphones

The sales tax rate in a city is 7.27%. How much sales tax is charged on a purchase of 5 headphones at $47.44 each? What is the total price?
[U]First, calculate the pre-tax price:[/U]
Pre-tax price = Price per headphone * Number of Headphones
Pre-tax price = $47.44 * 5
Pre-tax price = $237.20
Now calculate the tax amount:
Tax Amount = Pre-Tax Price * (Tax Rate / 100)
Tax Amount = $237.20 * 7.27/100
Tax Amount = $237.20 * 0.0727
Tax Amount = [B]$17.24
[/B]
Calculate the total price:
Total Price = Pre-Tax price + Tax Amount
Total Price = $237.20 + $17.24
Total Price = [B]$254.44[/B]

the sum of doubling a number and 100 which totals to 160

the sum of doubling a number and 100 which totals to 160
Take this algebraic expression in pieces:
[LIST=1]
[*]Let the number be n.
[*]Double it, means we multiply n by 2: 2n
[*]The sum of this and 100 means we add 100 to 2n: 2n + 100
[*]The phrase [I]which totals[/I] means we set 2n + 100 equal to 160
[/LIST]
[B]2n + 100 = 160[/B] <-- This is our algebraic expression
If the question asks you to solve for n, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B100%3D160&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]n = 30[/B]

The sum of twice an integer and 3 times the next consecutive integer is 48

The sum of twice an integer and 3 times the next consecutive integer is 48
Let the first integer be n
This means the next consecutive integer is n + 1
Twice an integer means we multiply n by 2:
2n
3 times the next consecutive integer means we multiply (n + 1) by 3
3(n + 1)
The sum of these is:
2n + 3(n + 1)
The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48:
2n + 3(n + 1) = 48
Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48
We first need to simplify the expression removing parentheses
Simplify 3(n + 1): Distribute the 3 to each term in (n+1)
3 * n = (3 * 1)n = 3n
3 * 1 = (3 * 1) = 3
Our Total expanded term is 3n + 3
Our updated term to work with is 2n + 3n + 3 = 48
We first need to simplify the expression removing parentheses
Our updated term to work with is 2n + 3n + 3 = 48
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(2 + 3)n = 5n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
5n + 3 = + 48
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 3 and 48. To do that, we subtract 3 from both sides
5n + 3 - 3 = 48 - 3
[SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE]
5n = 45
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5n/5 = 45/5
Cancel the 5's on the left side and we get:
n = [B]9[/B]

The team A scored 13 more points than Team B. The total of their score was 47. How many points did t

The team A scored 13 more points than Team B. The total of their score was 47. How many points did team A score?
Let a be the amount of points A scored, and b be the amount of points B scored. We're given:
[LIST=1]
[*]a = b + 13
[*]a + b = 47
[/LIST]
Plug (1) into (2)
(b + 13) + b = 47
Combine like terms:
2b + 13 = 47
[URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B13%3D47&pl=Solve']Typing this equation into our search engine[/URL], we get:
b = 17
Now plug this into (1):
a = 17 + 13
a = [B]30[/B]

The temperature dropped 2 every hours for 6 hours. What was the total number of degrees the temperat

The temperature dropped 2 every hours for 6 hours. What was the total number of degrees the temperature changed in the 6 hours
2 degrees drop per hour * 6 hours = [B]12 degree drop[/B]

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. h

The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins?
Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given:
[LIST=1]
[*]a + h + c = 48
[*]a = 0.5h
[*]a = c + 4
[/LIST]
To isolate equations in terms of Suresh's age (a), let's do the following:
[LIST]
[*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4
[*]Rewriting (2) by multiply each side by 2, we have h = 2a
[/LIST]
We have a new system of equations:
[LIST=1]
[*]a + h + c = 48
[*]h = 2a
[*]c = a - 4
[/LIST]
Plug (2) and (3) into (1)
a + (2a) + (a - 4) = 48
Group like terms:
(1 + 2 + 1)a - 4 = 48
4a - 4 = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]a = 13 [/B]<-- Suresh's age
This means that Hakima's age, from modified equation (2) above is:
h = 2(13)
[B]h = 26[/B] <-- Hakima's age
This means that Saad's age, from modified equation (3) above is:
c = 13 - 4
[B]c = 9[/B] <-- Saad's age
[B]
[/B]

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your

The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet.
We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets:
C(b) = nb + 9
We are given C(9) = 72 and b = 9
9n + 9 = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=9n%2B9%3D72&pl=Solve']Run this through our equation calculator[/URL], and we get [B]n = 7[/B].

The total cost of 100 dresses is $1,500.00. The mark-up is estimated at 20% of the unit cost, the pr

The total cost of 100 dresses is $1,500.00. The mark-up is estimated at 20% of the unit cost, the price of a single dress using the cost-plus method will be
The phrase [I]unit cost[/I] means price per one unit.
[U]Unit cost for one dress is:[/U]
Price of dresses / Number of dresses
1500/100
15
Each dress cost $15 which is the unit cost
[U]Cost plus method:[/U]
Cost plus price = Unit price + Unit price * markup
Cost plus price = 15 + 15 * 20%
Cost plus price = 15 + 3
Cost plus price = [B]$18
[MEDIA=youtube]H9rOp592y5s[/MEDIA][/B]

The total cost of producing x units for which the fixed cost are $2500 and the cost per unit $20

The total cost of producing x units for which the fixed cost are $2500 and the cost per unit $20
Total Cost = Cost per Unit * Units + Fixed Cost
Total Cost = [B]20x + 2500[/B]

The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25

The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25
Set up the cost function per x units:
[B]C(x) = 2900 + 25x[/B]

The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour

The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour how many hours were there:
Set up a cost function where h is the number of hours:
7h + 10 = 45
To solve for h, we t[URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']ype this equation into our search engine[/URL] and we get:
h = [B]5[/B]

the total number of fish if you had 8 and bought 4 more

the total number of fish if you had 8 and bought 4 more
If you have 8, and buy 4 more, this means you add. So we have:
8 fish + 4 fish = [B]12 fish[/B].

the total of 3 times the cube of u and the square of u

the total of 3 times the cube of u and the square of u
[U]The cube of u means we raise u to the power of 3:[/U]
u^3
[U]The square of u means we raise u to the power of 2:[/U]
u^2
The total of both of these is found by adding them together:
[B]u^3 + u^2[/B]

the total of a and 352 equals a divided by 195

the total of a and 352 equals a divided by 195
Take this algebraic expression in 3 parts:
[LIST=1]
[*]The total of a and 352 means we add 352 to a: a + 352
[*]a divided by 195: a/195
[*]The phrase [I]equals[/I] means we set (1) equal to (2) to get our final algebraic expression:
[/LIST]
[B]a + 352 = a/195[/B]

The total of z and 12 multiplied by the difference of 9 and y

The total of z and 12 multiplied by the difference of 9 and y
The total of z and 12:
z + 12
The difference of 9 and y:
9 - y
Now we multiply z + 12 by 9 - y:
[B](z + 12)(9 - y)[/B]

The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters

The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter?
Let q be the number of quarters. Let d be the number of dimes. We're given:
[LIST=1]
[*]q = 2d
[*]0.10d + 0.25q = 18
[/LIST]
Substitute (1) into (2):
0.10d + 0.25(2d) = 18
0.10d + 0.5d = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=0.10d%2B0.5d%3D18&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 30[/B].

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash t

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?
Set up the earnings equation for the volleyball team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 4w + 81
Set up the earnings equation for the wrestling team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 2w + 85
If the raised the same amount in total, set both earnings equations equal to each other:
4w + 81 = 2w + 85
Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides
4w + 81 - 2w = 2w + 85 - 2w
[SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE]
2w + 81 = 85
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 81 and 85. To do that, we subtract 81 from both sides
2w + 81 - 81 = 85 - 81
[SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE]
2w = 4
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 4/2
w = [B]2 <-- How many cars it will take
[/B]
To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2:
E = 4(2) + 81
E = 8 + 81
E = [B]89 <-- Total Earnings[/B]

The ———— of 5 and 7 is 12

The ———— of 5 and 7 is 12
[B](sum) or (total) since 5 + 7 = 12[/B]

There are 1 carrot, 3 onions, and 2 potatoes in a sink. What fraction of the vegetables are onions

There are 1 carrot, 3 onions, and 2 potatoes in a sink. What fraction of the vegetables are onions?
We have 1 + 3 + 2 = 6 total vegetables.
Which means we have 3/6 onions. But, we can reduce this fraction.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Simplifying 3/6 using our fraction simplifier[/URL], we get 1/2.

There are 113 identical plastic chips numbered 1 through 113 in a box. What is the probability of re

There are 113 identical plastic chips numbered 1 through 113 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is greater than 44?
We want 45, 46, … 113
That is 69 possible numbers. We draw this out of a total of 113
69/113 = 0.610619

There are 15 houses in a neighborhood. Nine of the houses have 6 people in them. The remaining house

There are 15 houses in a neighborhood. Nine of the houses have 6 people in them. The remaining houses have 4 people in them. How many people are in a neighborhood.
9 houses * 6 people per house = 54 people
The remaining houses equal 15 total houses - 9 houses = 6 houses
6 houses remaining times 4 people in each house = 24 people
54 people + 24 people = [B]78 people in the neighborhood[/B]

There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many piec

There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?
Total chalk pieces = Number of Chalkboards * Chalk pieces per chalkboard
Total chalk pieces = 2 * 2
Total chalk pieces = [B]4[/B]

There are 2.5 servings in a can of tuna fish. how many servings are there in 7 cans?

There are 2.5 servings in a can of tuna fish. how many servings are there in 7 cans?
Total Servings = Servings per can * number of cans
Total Servings = 2.5 * 7
Total Servings = [B]17.5 servings[/B]

There are 250 boys and 150 girls in a school, if 60% of the boys and 40% of the girls play football,

There are 250 boys and 150 girls in a school, if 60% of the boys and 40% of the girls play football, what percentage of the school play football
[U]First calculate total students:[/U]
Total students = Boys + Girls
Total students = 250 + 150
Total students = 400
[U]Calculate the boys that play football:[/U]
Boys playing football = 60% * 250
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=250&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Boys playing football [/URL]= 150
[U]Calculate the girls that play football:[/U]
Girls playing football = 40% * 150
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=40&den1=150&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Girls playing football[/URL][URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=250&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate'] [/URL]= 60
[U]Calculate total people playing football[/U]:
Total people playing football = Boys playing football + Girls playing football
Total people playing football = 150 + 60
Total people playing football = 210
Calculate percentage of the school playing football (P):
P = 100% * Total people playing football / Total Students
P = 100% * [URL='https://www.mathcelebrity.com/longdiv.php?num1=210&num2=400&pl=Long%20Division%20%28Decimals%29']210/400[/URL]
P = 100% * 0.525
P = [B]52.5%[/B]

There are 3,742,450 men, 3,177,805 women and 21,508 children in a village. Find the total population

There are 3,742,450 men, 3,177,805 women and 21,508 children in a village. Find the total population of the village.
Total population = Men + Women + Children
Total population = 3,742,450 + 3,177,805 + 21,508
Total population = [B]6,941,763[/B]

There are 32 students in a class. Nine of those students are women. What percent are men

There are 32 students in a class. Nine of those students are women. What percent are men
[U]Find the number of male students:[/U]
Males = Total Students - Females
Males = 32 - 9
Males = 23
[U]Calculate percentage of males:[/U]
Percentage of males = 100% * Males / Total Students
Percentage of males = 100% * 23 / 32
Percentage of males = 100% * 0.71875
Percentage of males = 71.88%
[URL='https://www.mathcelebrity.com/perc.php?num=23&den=32&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']See this link as well[/URL]

There are 4 people at a party. Each person brings one gift for each other person. What is the total

There are 4 people at a party. Each person brings one gift for each other person. What is the total number of gifts at the party?
Each person brings 3 gifts, 1 for each person other than themselves.
4 people x 3 gifts each = [B]12 total gifts[/B]

There are 480 calories per hour. An officer swims 1.5 hours for 30 days. How many calories is that?

There are 480 calories per hour. An officer swims 1.5 hours for 30 days. How many calories is that?
1.5 hours per day times 30 days = 45 total hours.
480 calories per hour times 45 total hours = [B]21,600 total calories[/B].

There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more th

[SIZE=4]There are 5 pencil-cases on the desk. Each pencil-case contains at least 10 pencils, but not more than 14 pencils. Which of the following could be the total number of pencils in all 5 cases?
A) 35
B) 45
C) 65
D) 75
[U]Determine the minimum amount of pencils (At least means greater than or equal to):[/U]
Minimum Amount of pencils = Cases * Min Quantity
Minimum Amount of pencils = 5 * 10
Minimum Amount of pencils = 50
[SIZE=4][U]Determine the maximum amount of pencils (Not more than means less than or equal to):[/U]
Maximum Amount of pencils = Cases * Min Quantity
Maximum Amount of pencils = 5 * 14
Maximum Amount of pencils = 70[/SIZE]
So our range of pencils (p) is:
50 <= p <= 70
Now take a look at our answer choices. The only answer which fits in this inequality range is [B]C, 65[/B].
[B][/B][/SIZE]

There are 60 students in a class. Three-fourths of them are girls. How many boys are there

There are 60 students in a class. Three-fourths of them are girls. How many boys are there
In the class, we have either boys or girls.
Total students = 60
3/4 of 60 = 60 * 3/4
Since 60/4 = 15, we have:
15 * 3 = 45 girls
Boys = 60 - girls
Boys = 60 - 45
Boys = [B]15[/B]

There are 8 lions, 4 tigers, 5 cheetahs, 6 giraffes, 7 hippos, and 78 monkeys at the City Zoo. If ea

There are 8 lions, 4 tigers, 5 cheetahs, 6 giraffes, 7 hippos, and 78 monkeys at the City Zoo. If each of the 4 zookeepers feeds the same number of animals, how many animals does each zookeeper feed?
Calculate Total Animals:
8 + 4 + 5 + 6 + 7 + 78 = 108
Now divide 108 animals equally into 4 zookeepers
108/4 = [B]27 animals each zookeeper will feed[/B]

There are 85 students in a class, 40 of them like math,31 of them like science, 12 of them like both

There are 85 students in a class, 40 of them like math,31 of them like science, 12 of them like both, how many don't like either.
We have the following equation:
Total Students = Students who like math + students who like science - students who like both + students who don't like neither.
Plug in our knowns, we get:
85 = 40 + 31 - 12 + Students who don't like neither
85 = 59 + Students who don't like neither
Subtract 59 from each side, we get:
Students who don't like neither = 85 - 59
Students who don't like neither = [B]26[/B]

there are 9 apples in each box. how many apples are in 6 boxes

there are 9 apples in each box. how many apples are in 6 boxes
Total apples = Number of boxes * apples per box
Total apples = 6 * 9
Total apples = [B]54[/B]

There are cows and chickens in a barn along with a three-legged dog named Tripod. If there are twice

There are cows and chickens in a barn along with a three-legged dog named Tripod. If there are twice as many chickens as cows, how many legs are there in the barn. (Call the number of cows n.)
Number of cows = n
Number of cows legs = 4n
Number of chickens = 2n
Number of chicken legs = 2*2n = 4n
Tripod legs = 3
Total legs = 4n + 4n + 3
[B]8n + 3[/B]

There are only horses and ducks on a farm. There are 80 animals in all and the number of ducks is ca

There are only horses and ducks on a farm. There are 80 animals in all and the number of ducks is called n. How many horse legs are there on the farm?
Number of duck legs = 2 legs * n ducks = 2n legs
Number of horses = 80 - n
Legs per horse = 4
Total horse legs = 4(80 - n) = [B]320 - 4n[/B]

There are y horses and z chickens in a barn. How many legs are there in the barn?

There are y horses and z chickens in a barn. How many legs are there in the barn?
[U]For total legs, we have:[/U]
Total Legs = Horse Legs + Chicken Legs
Total Legs = Legs per horse * number of horses + Legs per chicken * number of chickens
[U]Horses have 4 legs and chickens have 2 legs. We have y horses and z chickens. Plugging this in, we have:[/U]
Total Legs = [B]4y + 2z[/B]

There is a bag filled with 3 blue, 4 red and 5 green marbles. A marble is taken at random from the

There is a bag filled with 3 blue, 4 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting exactly 1 green?
Calculate Total marbles
Total marbles = Blue + Red + Green
Total marbles = 3 + 4 + 5
Total marbles = 12
Probability of a green = 5/12
Probability of not green = 1 - 5/12 = 7/12
To get exactly one green in two draws, we either get a green, not green, or a not green, green
[U]First Draw Green, Second Draw Not Green[/U]
[LIST]
[*]1st draw: Probability of a green = 5/12
[*]2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble
[*]To get the probability of the event, since each draw is independent, we multiply both probabilities
[*]Probability of the event is (5/12) * (7/11) = 35/132
[/LIST]
[U]First Draw Not Green, Second Draw Not Green[/U]
[LIST]
[*]1st draw: Probability of not a green = 7/12
[*]2nd draw: Probability of not green = 5/11 <-- 11 since we did not replace the first marble
[*]To get the probability of the event, since each draw is independent, we multiply both probabilities
[*]Probability of the event is (7/12) * (5/11) = 35/132
[/LIST]
To get the probability of exactly one green, we add both of the events:
First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green
35/132 + 35/132 = 70/132
[URL='https://www.mathcelebrity.com/fraction.php?frac1=70%2F132&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL], we get:
[B]35/66[/B]

There is a bag filled with 4 blue, 3 red and 5 green marbles. A marble is taken at random from the

There is a bag filled with 4 blue, 3 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting 2 blues?
We have (4 blue + 3 red + 5 green) = 12 total marbles
With replacement, the probability of getting one blue is 4/12 = 1/3
Since each draw is independent of the last, the probability of Blue, Blue = 1/3 * 1/3 = [B]1/9[/B]

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the b

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue?
Find the total number of marbles in the bag:
Total marbles = 5 blue + 6 red + 2 green
Total marbles = 13
The problem asks for exactly one blue in 2 draws [I]with replacement[/I]. Which means you could draw as follows:
Blue, Not Blue
Not Blue, Blue
The probability of drawing a blue is 5/13, since we replace the marbles in the bag each time.
The probability of not drawing a blue is (6 + 2)/13 = 8/13
And since each of the 2 draws are independent of each other, we multiply the probability of each draw:
Blue, Not Blue = 5/13 * 8/13 =40/169
Not Blue, Blue = 8/13 * 5/13 = 40/169
We add both probabilities since they both count under our scenario:
40/169 + 40/169 = 80/169
Checking our [URL='https://www.mathcelebrity.com/fraction.php?frac1=80%2F169&frac2=3%2F8&pl=Simplify']fraction simplification calculator[/URL], we see you cannot simplify this fraction anymore.
So our probability stated in terms of a fraction is 80/169
[URL='https://www.mathcelebrity.com/perc.php?num=80&den=169&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']Stated in terms of a decimal[/URL], it's 0.4734

There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult

There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult tickets are $8, tell me how many tickets were sold if gate receipts totaled $1028?
Let s be the number of student tickets and a be the number of adult tickets. We are given:
a + s = 175
8a + 5s = 1028
There are 3 ways to solve this, all of which give us:
[B]a = 51
s = 124
[/B]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Substitution']Substitution Method[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Elimination']Elimination Method[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Cramers+Method']Cramers Method[/URL]

There were 286,200 graphic designer jobs in a country in 2010. It has been projected that there will

There were 286,200 graphic designer jobs in a country in 2010. It has been projected that there will be 312,500 graphic designer jobs in 2020. (a) Using the data, find the number of graphic designer jobs as a linear function of the year.
[B][U]Figure out the linear change from 2010 to 2020[/U][/B]
Number of years = 2020 - 2010
Number of years = 10
[B][U]Figure out the number of graphic designer job increases:[/U][/B]
Number of graphic designer job increases = 312,500 - 286,200
Number of graphic designer job increases = 26,300
[B][U]Figure out the number of graphic designer jobs added per year[/U][/B]
Graphic designer jobs added per year = Total Number of Graphic Designer jobs added / Number of Years
Graphic designer jobs added per year = 26,300 / 10
Graphic designer jobs added per year = 2,630
[U][B]Build the linear function for graphic designer jobs G(y) where y is the year:[/B][/U]
G(y) = 286,200 + 2,630(y - 2010)
[B][U]Multiply through and simplify:[/U][/B]
G(y) = 286,200 + 2,630(y - 2010)
G(y) = 286,200 + 2,630y - 5,286,300
[B]G(y) = 2,630y - 5,000,100[/B]

Three people went to lunch and bought a large meal which they all split. The total cost, including t

Three people went to lunch and bought a large meal which they all split. The total cost, including tip, was $30. Each person paid $10 to the waitress and started to leave the restaurant. As they left, the waitress came running up to them with five dollars saying that she made a mistake and that the meal and tip should have cost only $25.
The waitress then gave each person one dollar, but didn't know how to split the remaining two dollars. They told her to keep the extra two dollars as an additional tip.
When the people started talking about what had just happened, they started getting confused. They had each paid $10 for the meal and received one dollar back, so they each really paid $9 for the meal for a total of $27. Add the two dollars of extra tip and the total is $29. Where did the extra one dollar go?
[B]The missing dollar is not really missing. The cost of the meal is really $27. The $25 plus the extra two dollar tip was given to the waitress -- $27
What we have is the cost ($27) plus the refund ($3) = $30.
The $30 that was originally paid is accounted for as follows:
Restaurant + regular waitress tip: $25
Three people: $3 (refund)
Waitress: $2 (extra tip)
$25 + $3 + $2 = $30[/B]

Tickets for a concert were priced at $8 for students and $10 for nonstudents. There were 1340 ticket

Tickets for a concert were priced at $8 for students and $10 for nonstudents. There were 1340 tickets sold for a total of $12,200. How many student tickets were sold?
Let s be the number of student tickets and n be the number of nonstudent tickets:
[LIST=1]
[*]n + s = 1340
[*]10n + 8s = 12200
[/LIST]
Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+s+%3D+1340&term2=10n+%2B+8s+%3D+12200&pl=Cramers+Method']simultaneous equation calculator[/URL]:
n = 740
[B]s = 600[/B]

Tim caught 6 ladybugs. Ali caught 7 and Jon caught 5. The children put some of their ladybugs in a b

Tim caught 6 ladybugs.
Ali caught 7 and Jon caught 5.
The children put some of their ladybugs in a big jar.
The jar then had 8 ladybugs.
How many ladybugs were not placed in the jar?
Add up the total ladybugs caught:
Total ladybugs caught = Tim's ladybugs + Ali's ladybugs + Jon's ladybugs
Total ladybugs caught = 6 + 7 + 5
Total ladybugs caught = 18
If the jar has 8 ladybugs, then the amount not in the jar is:
Amount of ladybugs not in the jar = Total ladybugs caught - Amount of ladybugs in the jar
Amount of ladybugs not in the jar = 18 - 8
Amount of ladybugs not in the jar = [B]10[/B]

Tip

Free Tip Calculator - Calculates the total bill with Tip and how much each person owes if the bill is split evenly. Shows the amount of tip per person.

To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total

To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total of $210 for her gym membership so far. How long has Maria been a member to the gym?
The cost function C(m) where m is the number of months for the gym membership is:
C(m) = 30m + 60
We're given that C(m) = 210 for Maria. We want to know the number of months (m) that Maria has been a member.
With C(m) = 210, we have:
30m + 60 =210
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30m%2B60%3D210&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]5[/B]

To buy a minivan you can pay $12,500 cash or put down $5000 and make 24 monthly payments of $698.05.

To buy a minivan you can pay $12,500 cash or put down $5000 and make 24 monthly payments of $698.05. How much would you save by paying cash?
[U]Calculate the total amount with payments:[/U]
Total Amount with payments = Payment Amount * Total Payments
Total Amount with payments = $698.05 * 24
Total Amount with payments = $16,753.20
[U]Calculate the total amount saved by paying cash:[/U]
Savings by paying cash = Total Amount with payments - Cash Payment
Savings by paying cash = $16,753.20 - $12,500
Savings by paying cash = [B]$4,253.20[/B]

To create an entry code, you must first choose 2 letters and then, 4 single-digit numbers. How ma

To create an entry code, you must first choose 2 letters and then, 4 single-digit numbers. How many different entry codes can you create?
List total combinations using the product of all possibilities:
26 letters * 26 letters * 10 digits (0-9) * 10 digits (0-9) * 10 digits (0-9) * 10 digits (0-9)
[B]6,760,000[/B]

Todd bought 5 ice cream sandwiches for $3.75. Bryce bought one ice cream sandwich for $1.00. Who got

Todd bought 5 ice cream sandwiches for $3.75. Bryce bought one ice cream sandwich for $1.00. Who got the better deal?
Todd's unit cost is found by:
Todd's Unit Cost = Total Price / Total Ice Cream Sandwiches
Todd's Unit Cost = $3.75/5
Todd's Unit Cost = $0.75
Bryce's unit cost is $1.00 per ice cream sandwich, so [B]Todd got the better deal.[/B]

Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount

Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount of his sales. What were his sales last month if he earned a total of $4500?
Let total sales be s. We're given the following earnings equation:
0.03s + 2250 = 4500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.03s%2B2250%3D4500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]75,000[/B]

total of a number and the square of a number

total of a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The square of a number means we raise x to the power of 2. x^2
The total means we add x squared to x:
[B]x + x^2[/B]

Total of a number v and 1

[I]Total[/I] means we add
[B]v + 1[/B]

Total Revenue

Free Total Revenue Calculator - Given a quantity, price, and item, this calculates the total revenue.

Tristan is making smoothies. Each smoothie uses 54 cup of yogurt. How many cups of yogurt does he ne

Tristan is making smoothies. Each smoothie uses 54 cup of yogurt. How many cups of yogurt does he need to make 13 smoothies? Express your answer in simplest form.
Total Cups = Number of smoothies * cups of yogurt per smoothie
Total Cups =13 * 54
Total Cups = [B]702 cups[/B]

Two coins are flipped 2 times. Calculate the total outcomes of these coins.

Two coins are flipped 2 times. Calculate the total outcomes of these coins.
2 coins * 2 outcomes per coin = 4 possible outcomes
[LIST=1]
[*][B]H,H[/B]
[*][B]H,T[/B]
[*][B]T,H[/B]
[*][B]T,T[/B]
[/LIST]

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worke

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour?
Set up two equations:
(1) 10x + 5y = 1225
(2) x + y = 170
Rearrange (2)
x = 170 - y
Substitute that into (1)
10(170 - y) + 5y = 1225
1700 - 10y + 5y = 1225
1700 - 5y = 1225
Move 5y to the other side
5y + 1225 = 1700
Subtract 1225 from each side
5y =475
Divide each side by 5
[B]y = 95[/B]
Which means x = 170 - 95, [B]x = 75[/B]

Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked

Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked for 15 hours. Together they charged a total of $2375. What was the rate charged per hour by each mechanic if the sum of the two rates was $235 per hour?
Setup equations where x is the rate of the first mechanic and y is the rate of the second mechanic:
[LIST]
[*]5x + 15y = 2375
[*]x + y = 235
[/LIST]
Using Cramers method with our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=5x+%2B+15y+%3D+2375&term2=x+%2B+y+%3D+235&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[LIST]
[*][B]x = 115[/B]
[*][B]y = 120[/B]
[/LIST]

Two numbers that total 44 and have a difference of 6

Two numbers that total 44 and have a difference of 6.
Let the two numbers be x and y. We're given the following equations:
[LIST=1]
[*]x + y = 44 <-- Total means a sum
[*]x - y = 6
[/LIST]
Add the two equations together:
(x + x) + (y - y) = 44 + 6
Cancelling the y terms, we have:
2x = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D50&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]x = 25
[/B]
Rearranging equation (2) above, we get:
y = x - 6
Substituting x = 25 into this, we get:
y = 25 - 6
[B]y = 19[/B]

Two numbers total 12, and their differences is 20. Find the two numbers.

Two numbers total 12, and their differences is 20. Find the two numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + y = 12
[*]x - y = 20
[/LIST]
Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together:
(x + x) + (y - y) = 12 + 20
The y terms cancel, so we have:
2x = 32
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D32&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]16[/B]
Substitute this value of x = 16 back into equation 1:
16 + y = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=16%2By%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get:
y = [B]-4
[/B]
Now, let's check our work for both equations:
[LIST=1]
[*]16 - 4 = 12
[*]16 - -4 --> 16 + 4 = 20
[/LIST]
So these both check out.
(x, y) = ([B]16, -4)[/B]

Two numbers total 50 and have a difference of 28. Find the two numbers.

Two numbers total 50 and have a difference of 28. Find the two numbers.
Using x and y as our two numbers, we write the following 2 equations:
[LIST=1]
[*]x + y = 50
[*]x - y = 28
[/LIST]
Add the 2 rows:
2x = 78
Divide each side by 2:
[B]x = 39[/B]
If x = 39, then from (1), we have
y = 50 - 39
[B]y = 11[/B]

two unbiased dice are thrown. find the probability that the total number on the dice is greater than

two unbiased dice are thrown. find the probability that the total number on the dice is greater than 10
[URL='http://www.mathcelebrity.com/2dice.php?gl=2&pl=10&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']From our 2 dice calculator[/URL]:
We have (5,6),(6,5),(6,6)
P(Sum) > 10 is [B]1/12[/B]

Two years of local internet service costs 685, including the installation fee of 85. What is the mon

Two years of local internet service costs 685, including the installation fee of 85. What is the monthly fee?
Subtract the installation fee of 85 from the total cost of 685 to get the service cost only:
685 - 85 = 600
Now, divide that by 24 months in 2 years to get a per month fee
600/24 = [B]25 per month[/B]

Ty uses his blocks to build towers of 10 blocks each. There are 14 towers and five blocks left over

Ty uses his blocks to build towers of 10 blocks each. There are 14 towers and five blocks left over.
Total Blocks = Tower Blocks + Left Over Blocks
[U]First, calculate the number of tower blocks:[/U]
Tower Blocks = Towers * Blocks per Tower
Tower Blocks = 14 * 10
Tower Blocks = 140
[U]We have 5 left over blocks, so we calculate our total blocks:[/U]
Total Blocks = 140 + 5
Total Blocks = [B]145[/B]

Utility and Cost Utility Ratio

Free Utility and Cost Utility Ratio Calculator - Given 2 methods with a set of utilities and weights/probabilities, this will calculate the utility for each method, as well as the total utility using the additive method, as well as the Cost Utility Ratio

Vacation is 72 days long. What percent of the entire year is summer vacation ?

Vacation is 72 days long. What percent of the entire year is summer vacation ?
Vacation day Percent = 100% * Vacation Days / Total Days in the year
Vacation day Percent = 100% * 72/365
Vacation day Percent = 100% * [URL='https://www.mathcelebrity.com/perc.php?num=72&den=365&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']0.1973[/URL]
Vacation day Percent = [B]19.73%[/B]

Wan bought 2 salad rolls and 1 bottle of orange juice. If each salad roll costs x cents and the oran

Wan bought 2 salad rolls and 1 bottle of orange juice. If each salad roll costs x cents and the orange juice costs $1.50, write the expression for the total cost (in cents) for the food and drink
The cost C is:
C = 2x + 1.50(1)
Simplify:
[B]C = 2x + 1.50[/B]

What can we conclude if the coefficient of determination is 0.94?

What can we conclude if the coefficient of determination is 0.94?
[LIST]
[*]Strength of relationship is 0.94
[*]Direction of relationship is positive
[*]94% of total variation of one variable(y) is explained by variation in the other variable(x).
[*]All of the above are correct
[/LIST]
[B]94% of total variation of one variable(y) is explained by variation in the other variable(x)[/B]. The coefficient of determination explains ratio of explained variation to the total variation.

What is the average of 7 consecutive numbers if the smallest number is called n?

What is the average of 7 consecutive numbers if the smallest number is called n?
[LIST]
[*]First number = n
[*]Second number = n + 1
[*]Third number = n + 2
[*]Fourth number = n + 3
[*]Fifth number = n + 4
[*]Sixth number = n + 5
[*]Seventh number = n + 6
[/LIST]
Average = Sum of all numbers / Total numbers
Average = (n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 + n + 6)/7
Average = 7n + 21/7
Factor out a 7 from the top:
7(n + 3)/7
Cancel the 7's:
[B]n + 3[/B]

When Esteban left for college, his parents decided to give him an allowance of $100 every 4 weeks. T

When Esteban left for college, his parents decided to give him an allowance of $100 every 4 weeks. They told Esteban that he could decide how he wanted raises to his allowance determined.
Choice #1 - A raise of $10 every 4 weeks
Choice #2 - A raise of $1.50 each week
What choice should Esteban pick?
Choice 1:
[LIST]
[*]First 4 weeks = $100
[*]Weeks 5 - 8 = $110
[*]Weeks -9-12 = $120
[*]Total = $330
[/LIST]
Choice 2:
[LIST]
[*]1st week = $25
[*]2nd week = $26.50
[*]3rd week = $28
[*]4th week - $29.50
[*]5th week = $31.00
[*]6th week = $32.50
[*]7th week = $34.00
[*]8th week = $35.50
[*]9th week = $37.00
[*]10th week = $38.50
[*]11th week = $40.00
[*]12th week = $41.50
[*]Total = [B]$399[/B]
[/LIST]
[B]Choice 2 is the better option[/B]

Which of the following is the probability that a green marble will be selected from a bag containing

Which of the following is the probability that a green marble will be selected from a bag containing 9 red marbles 6 blue marbles 7 green marbles and 11 yellow marbles if one is selected randomly?
Total marbles in the bag:
9 red + 6 blue + 7 green + 11 yellow = 33
P(Green) = Green Marbles / Total Marbles
P(Green) = [B]7/33[/B]

William has 75 peppermints. Viana has p fewer peppermints than William

William has 75 peppermints. Viana has p fewer peppermints than William
Fewer means less, so we subtract to get Viana's total peppermints:
[B]75 - p[/B]

Winnie earns an annual salary of $55,117. If she pays $3,715 a year in taxes and receives a paycheck

Winnie earns an annual salary of $55,117. If she pays $3,715 a year in taxes and receives a paycheck every other week, how much does Winnie receive from each paycheck?
Subtract the taxes to get Winnie's Total net pay:
Total Net Pay = Annual Salary - Annual Taxes
Total Net Pay =$55,117 - $3,715
Total Net Pay = $51,402
Now, if Winnie gets paid every other week, and there are 52 weeks in a year, then she gets paid 26 times.
Calculate single paycheck amount
Single Paycheck Amount = Total Net Pay / 26 payments
Single Paycheck Amount = $51,402 / 26
Single Paycheck Amount = [B]$1,977[/B]

Write a system of equations to describe the situation below, solve using any method, and fill in the

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Hugo is going to send some flowers to his wife. Somerville Florist charges $2 per rose, plus $39 for the vase. Dwaynes Flowers, in contrast, charges $3 per rose and $10 for the vase. If Hugo orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be? How many roses would there be?
Let r be the number of roses and C(r) be the cost function. The vase is a one-time cost.
Somerville Florist:
C(r) = 2r + 39
Dwaynes Flowers
C(r) = 3r + 10
Set them equal to each other:
2r + 39 = 3r + 10
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2r%2B39%3D3r%2B10&pl=Solve']equation calculator[/URL], we get:
[B]r = 29[/B]

x textbooks if one textbook costs $140

x textbooks if one textbook costs $140
Since cost = price * quantity, we have:
Total cost = Cost per textbook * number of text books
Total cost = [B]140x[/B]

Yesterday, Boris had 144 baseball cards. Today, he got m more. Using m, write an expression for the

Yesterday, Boris had 144 baseball cards. Today, he got m more. Using m, write an expression for the total number of baseball cards he has now.
144 and m more means we add
[B]144 + m[/B]

Yesterday, Kareem had n baseball cards. Today, he got 9 more. Using n, write an expression for the t

Yesterday, Kareem had n baseball cards. Today, he got 9 more. Using n, write an expression for the total number of baseball cards he has now.
9 more means we add 9 to n
[B]n + 9[/B]

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a

Yolanda wants to rent a boat and spend less than $41. The boat costs $8 per hour, and Yolanda has a discount coupon for $7 off. What are the possible numbers of hours Yolanda could rent the boat?
A few things to build this problem:
[LIST=1]
[*]Discount subtracts from our total
[*]Cost = Hourly rate * hours
[*]Less than means an inequality using the < sign
[/LIST]
Our inequality is:
8h - 7 < 41
To solve this inequality for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-7%3C41&pl=Solve']type it in our math engine[/URL] and we get:
h < [B]6[/B]

Yosemite National Park charges $7 per person for an all day admission to the park. The total cost fo

Yosemite National Park charges $7 per person for an all day admission to the park. The total cost for n people to go to the park all day is given by the expression 7n. 8 friends go to the park on Saturday. What is the total cost of admission?
We want to evaluate f(n) = 7n for n = 8
f(8) = 7(8) = [B]56[/B]

You and 6 friends went out for pizza. When the total amount was split, each person paid $3. How much

You and 6 friends went out for pizza. When the total amount was split, each person paid $3. How much was the total bill?
You and 6 friends means 7 total people. If the bill was split, everybody paid the same. We have:
7 people * $3 per person = [B]$21 total bill[/B]

You and a friend collect acorns from a field. After g minutes u have collected(10 + 2g) acorns and y

You and a friend collect acorns from a field. After g minutes u have collected(10 + 2g) acorns and your friend has collected (5g - 2) acorns. How many total acorns have you and your friend collected
Add both acorn collections together:
(10 + 2g) + (5g - 2)
Group like terms:
(5 + 2)g + 10 - 2
[B]7g + 8[/B]

You and some friends are going to the fair. Each ticket for a ride costs $0.75. If n is the number o

You and some friends are going to the fair. Each ticket for a ride costs $0.75. If n is the number of tickets purchased, write an expression that gives the total cost of buying n tickets.
We know cost = Price * Quantity, so we have:
Cost of buying n tickets = [B]0.75n[/B]

You are baking muffins for your class. There are 17 total students in your class and you have baked

You are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student.
2 muffins per student = 17*2 = 34 muffins.
We have an equation with a given 5 muffins, how much do we need (x) to get to 34 muffins (2 per student):
x + 5 = 34
To solve for x, we type this equation into our search engine and we get:
x = [B]29[/B]

You are baking muffins for your class. There are 17 total students in your class and you have baked

You are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student.
[U]Calculate total muffins:[/U]
Total muffins = 2 muffins per student * 17 students
Total muffins = 34
[U]Set up the equation using x for muffins:[/U]
[B]x + 5 = 34
[/B]
[U]To Solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B5%3D34&pl=Solve']type it in our search engine[/URL] and we get:[/U]
x = [B]29
[/B]

You are comparing the costs of producing shoes at two different manufacturers. Company 1 charges $5

You are comparing the costs of producing shoes at two different manufacturers. Company 1 charges $5 per pair of shoes plus a $650 flat fee. Company 2 charges $4 per pair of shoes plus a $700 flat fee. How many pairs of shoes are produced when the total costs for both companies are equal?
Let s be the number of shoes. We have two equations:
(1) C = 5s + 650
(2) C = 4s + 700
Set the costs equal to each other
5s + 650 = 4s + 700
Subtract 4s from each side
s + 650 = 700
Subtract 650 from each side
[B]s =50[/B]

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $2 for a ticket. Write an expression for the total cost of going to Cedar Point where r is the number of rides.
Set up the cost equation C(r):
C(r) = Cost per ride * r rides + Park Fee
[B]C(r) = 2r + 50[/B]

You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars.

You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars. You parked for 3.25 hours. What is the cost?
[U]Calculate the number of paid hours:[/U]
Paid Hours = Total Hours - 1 (since first hour is free)
Paid Hours = 3.25 - 1
Paid Hours = 2.25
[U]Calculate the total cost:[/U]
Total Cost = Hourly Rate * Paid Hours
Total Cost = 2 * 2.25
Paid Hours = [B]$4.50[/B]

You are selling fertilizer to female farmers in Ghana. There are 22,600,000 people in Ghana, and 60%

You are selling fertilizer to female farmers in Ghana. There are 22,600,000 people in Ghana, and 60% are of working age. Within that working-age group, women account for 53%. Of the working-age females, 42% of them are employed in farming. What is the total number of potential customers for your fertilizer?
[U]Our sample population is found by this product:[/U]
Female farmers of working age in Ghana = Total people in Ghana *[I] Working Age[/I] * Women of working Age * Farmers
Since 60% = 0.6, 53% = 0.53, and 42% = 0.42, we have
Female farmers of working age in Ghana = 22,600,000 * 0.6 * 0.53 * 0.42
Female farmers of working age in Ghana = [B]3,018,456[/B]

You bought a box of pens for $5 and some notepads for $3 each. You spent a total of $26.

You bought a box of pens for $5 and some notepads for $3 each. You spent a total of $26.
Let p be the number of pens and n be the number of notepads. Our equation is:
5[B]p + 3n = 26[/B]

You bought a magazine for $3 and some candy bars for $2 each. You spent a total of $19. How many can

You bought a magazine for $3 and some candy bars for $2 each. You spent a total of $19. How many candy bars did you buy?
Calculate the candy bar spend:
Candy bar spend = Total spend - magazine spend
Candy bar spend = 19 - 3
Candy bar spend = 16
Calculate number of candy bars:
Number of candy bars = Candy Bar Spend / Cost per candy bar
Number of candy bars = 16/2
Number of candy bars = [B]$8[/B]

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser co

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?
Subtract the cost of the magazine from what you spent:
$25 - $5 = $20.
If you spent $20 on 4 erasers, we divide 20/4 = [B]$5 per eraser[/B]

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser co

You bought a magazine for $5 and four erasers. You spent a total of $25. How much did each eraser cost?
[U]Calculate the cost of all erasers:[/U]
Cost of all erasers = Total Spend - Magazine Cost
Cost of all erasers = 25 - 5
Cost of all erasers = 20
[U]Calculate the cost per eraser:[/U]
Cost per eraser = Cost of all erasers / Total erasers
Cost per eraser = 20 / 4
Cost per eraser = Cost of all erasers / Total erasers
Cost per eraser = [B]$5[/B]

You bought a magazine for $5 and four erasers. You spent a total of $25.how much did each eraser cos

You bought a magazine for $5 and four erasers. You spent a total of $25.how much did each eraser cost?
[U]Calculate the cost of the erasers:[/U]
Cost of erasers = Total Spend - Magazine
Cost of erasers = 25 - 5
Cost of erasers = 20
[U]Calculate the cost per eraser:[/U]
Cost per eraser = Cost of erasers / Number of erasers
Cost per eraser = 20/4
Cost per eraser = [B]$5[/B]

You but a sandwich for $2.25, an a apple for $0.55, and a bottle of juice for $1.85 what is the tota

You but a sandwich for $2.25, an a apple for $0.55, and a bottle of juice for $1.85 what is the total cost
[U]Calculate total cost:[/U]
Total cost = Sandwich cost + apple cost + juice cost
Total cost = 2.25 + 0.55 + 1.85
Total cost = [B]$4.65[/B]

You buy 4 magazines for $5 each and 2 drinks for $4 each

You buy 4 magazines for $5 each and 2 drinks for $4 each
Calculate total cost:
Since cost = price * quantity, we have:
Total cost = $5 * 4 magazines + $4 * 2 drinks
Total cost = 20 + 8
Total Cost = [B]28[/B]

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food.
Our purchase includes at cat litter and cat food. Adding those together, we're given:
12.25 + x = 19.08
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=12.25%2Bx%3D19.08&pl=Solve']we type this equation into our search engine[/URL], and we get:
x = 6.83
Since the cat food includes sales tax, we need to remove the sales tax of 6% to get the original purchase price.
Original purchase price = After tax price / (1 + tax rate)
Original purchase price = 6.83/1.06
Original purchase price = [B]$6.44[/B]

You collect a total of 75 in donations from three people. The three donations are in the ratio 4:4:7

You collect a total of 75 in donations from three people. The three donations are in the ratio 4:4:7. How much is each of the smaller donations?
4 + 4 + 7 = 15
Each person's donation ratio is:
[LIST=1]
[*]Donation 1 is 4/15 of 75
[*]Donation 2 is 4/15 of 75
[*]Donation 3 is 7/15 of 75
[/LIST]
4/15(75) = 5 * 4 = 20
7/15(75) = 5 * 7 = 35
Each person's donation amount is:
[LIST=1]
[*][B]$20[/B]
[*][B]$20[/B]
[*][B]$35[/B]
[/LIST]
Check out work:
20 + 20 + 35 = 75!

You collect stamps. You give steven 21 stamps. At the end youbhave 3. How many stamps did you start

You collect stamps. You give steven 21 stamps. At the end youbhave 3. How many stamps did you start with?
You start with s stamps.
s
You give Steven 21. Giving means you subtract from your total:
s - 21
You have 3 left
s - 21 = 3
To solve this equation for s, we t[URL='https://www.mathcelebrity.com/1unk.php?num=s-21%3D3&pl=Solve']ype it in our math engine[/URL] and we get:
s = [B]24[/B]

You conduct 50,000 tests, 1500 people test positive, what's the positivity rate?

You conduct 50,000 tests, 1500 people test positive, what's the positivity rate?
[U]Our Positivity Rate formula is below:[/U]
Positivity Rate = 100% * positive tests / Total tests
[U]Plugging in our numbers from the problem, we get:[/U]
Positivity Rate = 100% * 1500/50000
Positivity Rate = 100% * 0.03
Positivity Rate = [B]3%[/B]

you draw a card at random from a deck that contains 3 black cards and 7 red cards what is the probab

you draw a card at random from a deck that contains 3 black cards and 7 red cards what is the probability of you drawing a black card
Total cards = 3 black + 7 red
Total cards = 10
P(Black) = Black cards / Total Cards
P(Black) = [B]3/10 or 0.3[/B]

You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per ho

You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per hour cleaning. You worked 9 more hours babysitting than cleaning. How many hours did you work last week?
Let b be the hours of babysitting and c be the hours of cleaning. We're given two equations:
[LIST=1]
[*]b = c + 9
[*]5b + 7c = 141
[/LIST]
Substitute equation (1) into (2):
5(c + 9) + 7c = 141
Multiply through:
5c + 45 + 7c = 141
Combine like terms:
12c + 45 = 141
[URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B45%3D141&pl=Solve']Typing this equation into our search engine[/URL], we get:
c = 8
Now substitute this value of c back into Equation (1):
b = 8 + 9
b = 17
The total hours worked (t) is:
t = b + c
t = 17 + 8
t = [B]25[/B]

You earned $400 at work today. You earn $50 per hour. How many hours did you work?

You earned $400 at work today. You earn $50 per hour. How many hours did you work?
Hours Worked = Total Earnings / Earnings per hour
Hours Worked = 400 / 50
Hours Worked = [B]8[/B]

You fly x miles and then drive y miles. How many miles did you travel?

You fly x miles and then drive y miles. How many miles did you travel?
Total miles traveled = fly miles + drive miles
Total miles traveled = [B]x + y[/B]

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 go to your favorite restaurant. The bill for the food is $74.26. The tax on the bill will be 9%.

You go to your favorite restaurant. The bill for the food is $74.26. The tax on the bill will be 9%. You are planning on giving a tip on that total amount (bill and tax together) of 20%. What is your final bill, all taxes and tips included?
[U]Calculate the after tax amount:[/U]
After tax amount = Bill * (1 + Tax Rate)
Since 9% = 0.09, we have:
After tax amount = 74.26 * (1 + 0.09)
After tax amount = 74.26 * 1.09
After tax amount = 80.94
[U]Calculate the Tip amount:[/U]
Tip amount = After tax amount * tip percent
Since 20% = 0.2, we have:
Tip amount = 80.94 * 0.20
Tip amount = 16.19
[U]Calculate the final bill:[/U]
Final Bill = After Tax Amount + Tip Amount
Final Bill = 80.94 + 16.19
Final Bill = [B]97.13[/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 had $21 to spend on three raffle tickets. After buying them you have $12. How much does each raf

You had $21 to spend on three raffle tickets. After buying them you have $12. How much does each raffle ticket cost?
If we have $12 left, we spent:
Total Raffle Spend = Total Spend - LeftOver spend
Total Raffle Spend = $21 - $12
Total Raffle Spend = $9
Calculate the cost per raffle ticket:
Cost per raffle ticket = Total Raffle Spend / Cost Per raffle ticket
Cost per raffle ticket = $9/3
Cost per raffle ticket = [B]$3[/B]

You have $110 saved in your bank account. You want to save $15 every week. Let x be the amount of we

You have $110 saved in your bank account. You want to save $15 every week. Let x be the amount of weeks and y be the total amount saved.
Savings mean we add to the bank balance, so we have:
[B]y = 15x + 110[/B]

You have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer.

You have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer.
Let k be the number of kilometers.
Total Cost = Cost per kilometer * number of kilometers + Fixed Cost
With k for kilometers, 2.5 as cost per kilometer, and 5 as fixed cost, and 20 on total cost, we have:
2.5k + 5 = 20
To solve this equation for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5k%2B5%3D20&pl=Solve']type it in our math engine [/URL]and we get
k = [B]6[/B]

You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per kilometer. Write the inequality

You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per kilometer. Write the inequality.
Let k be the number of kilometers. We want our total to be $20 [I]or less. [/I]We have the following inequality:
[B]2.50k + 5 <= 20[/B]

You have $535 in your wallet and want to buy pizzas that cost $3 each. How much money will you have

You have $535 in your wallet and want to buy pizzas that cost $3 each. How much money will you have left after buying 178 pizzas?
Calculate total cost of pizzas:
Cost = 178 * 3
Cost = 534
Determine money leftover
Money leftover = Money in Wallet - Cost of pizzas
Money leftover = 535 - 534
Money leftover = [B]1[/B]

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the rest of the money to buy shirts. Find the inequality.
Let j be the number of jeans. Let s be the number of shirts. We are given:
[LIST]
[*]Mom told you to buy one pair of jeans. So we have $80 to start with - $29 for 1 pair of jeans = $51 left over
[/LIST]
Now, since shirts cost $12 each, and our total number of shirts we can buy is s, our inequality is [B]12s <= 51[/B].
We want to find the s that makes this inequality true.
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12s%3C%3D51&pl=Show+Interval+Notation']Run this statement through our calculator[/URL], and we get s <= 4.25. But, we need s to be an integer, so we have s <= 4.

You have 36 marbles that are red, white and blue. If 12 of the marbles are red, and 13 of the marble

You have 36 marbles that are red, white and blue. If 12 of the marbles are red, and 13 of the marbles are blue, what fraction of marbles are white?
[U]Calculate the number of white marbles:[/U]
Number of white marbles = Total marbles - Red marbles - Blue marbles
Number of white marbles = 36 - 12 - 13
Number of white marbles = 11
[U]Calculate the fraction of white marbles:[/U]
Fraction of white marbles =Number of white marbles / Total marbles
Fraction of white marbles = [B]11/36[/B]

You have a total of 42 math and science problems for homework. You have 10 more math problems than s

You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?
Let m be the math problems and s be the science problems. We have two equations:
(1) m + s = 42
(2) m = s + 10
Substitute (2) into (1)
(s + 10) + s = 42
Combine like terms
2s + 10 = 42
Subtract 10 from each side
2s = 32
Divide each side by 2
[B]s = 16[/B]
So that means m = 16 + 10 --> [B]m = 26
(m, s) = (26, 16)[/B]

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes.

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes. You go to the store and find two shirts and three pairs of jeans you like. The two shirts are buy-one-get-one half off, at $22.35 each. The three pairs of jeans are buy-two-get-one-free, at $23.70.
Tax Rate for Harmonized Sales Tax is 13%
a. What would be the total for the two shirts (don’t forget to include taxes)?
b. What would be the total for the three pairs of jeans (don’t forget to include taxes)?
c. Which would you buy and why?
a. Half of 22.35 is 11.18
So two shirts cost:
22.35 + 11.18 = 33.53
Cost with Tax of 13% is:
33.53 * 1.13 = [B]37.89
[/B]
b. Three pairs of jeans are calculated by cost of 1 pair times 2 jeans and you get the third one free:
23.70 * 2 = 47.40
Cost with Tax of 13% is:
47.40 * 1.13 = [B]53.56
[/B]
c. Calculate unit cost, which is cost per item
Unit cost of Shirts = 37.89 / 2 = [B]18.95[/B]
Unit cost of Jeans = 53.56 / 3 = [B]17.85
Buy the jeans since they have a lower unit cost[/B]

You like to shovel snow in winter. You made them pay 7 dollars for every driveway you shoveled and e

You like to shovel snow in winter. You made them pay 7 dollars for every driveway you shoveled and earned 42 dollars. How many driveways did you shovel?
Driveways shoveled = Total Money / Dollars per Driveway
Driveways shoveled = 42/7
[URL='https://www.mathcelebrity.com/fraction.php?frac1=42%2F7&frac2=3%2F8&pl=Simplify']Driveways shoveled[/URL] = [B]6[/B]

You need to hire a catering company to serve meals to guests at a wedding reception. Company A charg

You need to hire a catering company to serve meals to guests at a wedding reception. Company A charges $500 plus $20 per guest. Company B charges $800 plus $16 per guest. For how many guests are the total costs the same at both companies?
Set up the Cost equations for both companies where g is the number of guests:
[LIST]
[*]C(a) = 20g + 500
[*]C(b) = 16g + 800
[/LIST]
Set each equation equal to each other and use our [URL='http://www.mathcelebrity.com/1unk.php?num=20g%2B500%3D16g%2B800&pl=Solve']equation solver[/URL] to get:
[B]g = 75[/B]

you own 15 CDs. you buy 7 more.How many CDs do you own now?

you own 15 CDs. you buy 7 more.How many CDs do you own now?
Start with 15
You buy 7 more, which means you [U]add[/U] 7 to your total:
15 + 7 = [B]22[/B]

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a monthly fee of 160.00. Write and equation that represents your total cost Y in dollars after X months.
Set up the cost function Y where x is the number of months you rent
[B]Y = 160x + 510[/B]

You practice the piano for 30 minutes each day. Write and solve an equation to find the total time t

You practice the piano for 30 minutes each day. Write and solve an equation to find the total time t you spend practicing the piano in a week.
Since there is 7 days in a week, we have:
t = 30 * 7
[B]t = 210[/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 roll a red die and a green die. What is the size of the sample space of all possible outcomes of

You roll a red die and a green die. What is the size of the sample space of all possible outcomes of rolling these two dice, given that the red die shows an even number and the green die shows an odd number greater than 1?
[LIST]
[*]Red Die Sample Space {2, 4, 6}
[*]Green Die Sample Space {3, 5}
[*]Total Sample Space {(2, 3), (2, 5), (4, 3), (4, 5), (6, 3), (6, 5)}
[*]The sie of this is 6 elements.
[/LIST]

You save $15 a week. How much will you have saved after w weeks?

You save $15 a week. How much will you have saved after w weeks?
Total savings = Savings per week * number of weeks
Total savings = [B]15w[/B]

You split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays

You split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays 4% annual interest. After one year, you have earned a total of $69.50 in interest. How much money did you invest in each account. Explain.
Let a be the amount you invest in Account A. So this means you invested 1500 - A in account B. We have the following equation:
05a + (1500 - a).04 = 69.50
Simplifying, we get:
0.05a + 1560 - 0.04a = 69.50
0.01a + 60 = 69.50
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.01a%2B60%3D69.50&pl=Solve']equation solver[/URL], we get:
[B]a = 950[/B]
So this means Account B is b = 1500 - 950 = [B]550[/B]

You started this year with $491 saved and you continue to save an additional $11 per month. Write an

You started this year with $491 saved and you continue to save an additional $11 per month. Write an algebraic expression to represent the total amount of money saved after m months.
Set up a savings function for m months
[B]S(m) = 491 + 11m[/B]

You want to put 520 quarters in coin wrappers. You need one wrapper for every $10 in quarters. Write

You want to put 520 quarters in coin wrappers. You need one wrapper for every $10 in quarters. Write an equation you can use to find how many wrappers w you need
First, calculate the number of quarters in $10:
Quarters in $10 = Value of Quarters / Cost per quarter
Quarters in $10 = 10/0.25
Quarters in $10 = 40
Now find out how many wrappers we need with each wrapper holding 40 quarters:
Number of wrappers = Total quarters / Quarters per wrapper
Number of wrappers =520/40
Number of wrappers = [B]13[/B]

You went to the State Fair and spent $20. If cotton candy costs $2 and a soda pop costs $1. Which eq

You went to the State Fair and spent $20. If cotton candy costs $2 and a soda pop costs $1. Which equation represents the relation between the number of cotton candy (c) and soda pops (s) you can buy?
Our total cost for 20 at the state fair is:
Cost of Cotton Candy + Cost of Soda = 20
We know that price = cost * quantity, so we have:
2c + 1s = 20
Since 1s is written as s, we have:
[B]2c + s = 20[/B]

you work at a carnival for 9.5 hours. You earn $99.75. How much do you earn per hour?

you work at a carnival for 9.5 hours. You earn $99.75. How much do you earn per hour?
Earnings per hour = Total Earnings / Total Hours Worked
Earnings per hour = $99.75 / 9.5
Earnings per hour = [B]$10.50[/B]

You work for a remote manufacturing plant and have been asked to provide some data about the cost of

You work for a remote manufacturing plant and have been asked to provide some data about the cost of specific amounts of remote each remote, r, costs $3 to make, in addition to $2000 for labor. Write an expression to represent the total cost of manufacturing a remote. Then, use the expression to answer the following question. What is the cost of producing 2000 remote controls?
We've got 2 questions here.
Question 1: We want the cost function C(r) where r is the number of remotes:
C(r) = Variable Cost per unit * r units + Fixed Cost (labor)
[B]C(r) = 3r + 2000
[/B]
Question 2: What is the cost of producing 2000 remote controls.
In this case, r = 2000, so we want C(2000)
C(2000) = 3(2000) + 2000
C(2000) = 6000 + 2000
C(2000) = [B]$8000[/B]

Your 14 gallon tank was filled for $32.06. What was the cost per gallon?

Your 14 gallon tank was filled for $32.06. What was the cost per gallon?
Cost per gallon = Total Cost / Gallons in Tank
Cost per gallon = 32.06 / 14
Cost per gallon = [B]2.29[/B]

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pi

Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase?
Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations:
[LIST=1]
[*]c + f = 10
[*]c + 1.5f = 12.50
[/LIST]
Rearrange equation 1 by subtracting f from both sides:
[LIST=1]
[*]c = 10 - f
[*]c + 1.5f = 12.50
[/LIST]
Substitute equation (1) into equation (2):
10 - f + 1.5f = 12.50
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=10-f%2B1.5f%3D12.50&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]f = 5[/B]
Now, substitute this f = 5 value back into modified equation (1) above:
c = 10 - 5
[B]c = 5[/B]

Youre setting sales goals for next month. You base your goals on previous average sales. The actual

Youre setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?
Find the average sales for the last four years:
Average Sales = Total Sales / 4
Average Sales = (24 + 30 + 23 + 27) / 4
Average Sales = 104 / 4
Average Sales = [B]26 units[/B]

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it tak

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it take for the population of about 600,000 to turn into zombies?
Let d = every 2 days. We set up the exponential equation
2 * 2^d = 600,000
Divide each side by 2:
2^d = 300000
To solve this equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=2%5Ed%3D300000&pl=Calculate']type it in our math engine[/URL] and we get
d = 18.19 (2 day periods)
18.19 * days per period = 36.38 total days
Most problems like this ask you to round to full days, so we round up to [B]37 days[/B].