Percentage - ACT Math
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There are n pennies in a jar. Let p represent the decimal ratio of the pennies that are dated before 1983. Which of the following equations repesents the number of pennies that are dated 1983 or later?
There are n pennies in a jar. Let p represent the decimal ratio of the pennies that are dated before 1983. Which of the following equations repesents the number of pennies that are dated 1983 or later?
The proportion of pennies before 1983 would be np. Therefore, the pennies dated 1983 or later would be n(1-p).
The proportion of pennies before 1983 would be np. Therefore, the pennies dated 1983 or later would be n(1-p).
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Students at a country fair typically spend \$40. The students have agreed to spend 40% less at this year's fair. Assuming all the students follow their new agreement, what is the most that could be spent by a student at this year's fair?
Students at a country fair typically spend \$40. The students have agreed to spend 40% less at this year's fair. Assuming all the students follow their new agreement, what is the most that could be spent by a student at this year's fair?
This is a percentage problem, so it is important to know that 40% of some value is equal to 0.4 of said value. So to find 40% of \$40, we multiply 40 * 0.40, which equals 16. This 16 represents 40% of the original value of \$40. So if a student was to spend 40% less than they usually spend, we would subtract \$16, which is 40% of the original value, from \$40, giving us an answer of \$24.
This is a percentage problem, so it is important to know that 40% of some value is equal to 0.4 of said value. So to find 40% of \$40, we multiply 40 * 0.40, which equals 16. This 16 represents 40% of the original value of \$40. So if a student was to spend 40% less than they usually spend, we would subtract \$16, which is 40% of the original value, from \$40, giving us an answer of \$24.
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Express the following as a decimal:
Express the following as a decimal:
To convert a percentage to a decimal, you must add a decimal two points to the left from the right hand side. Thus,
To convert a percentage to a decimal, you must add a decimal two points to the left from the right hand side. Thus,
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Which of the following is equivalent to 
?
Which of the following is equivalent to
To find a decimal from a percentage, divide the percentage value by 
. In this case, convert the fraction to a decimal first:
To find a decimal from a percentage, divide the percentage value by
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A 
share in a stock is added to a 
share by speculators. What is the decimal equivalent of the combined shares?
A
To convert from a percentage to a decimal, divide the decimal by 
. In this case, we can add the percentages first.
To convert from a percentage to a decimal, divide the decimal by
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Convert the following to a percentage.
Convert the following to a percentage.
To convert a fraction into a percentage, simply simplify the fraction into a decimal and multiply by 100.
To convert a fraction into a percentage, simply simplify the fraction into a decimal and multiply by 100.
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The girl's tennis team decided to do multiple fundraisers to raise enough to buy new equipment for next season. The following is a table of 4 of the fundraisers they did and the fraction of the total funds each raised.
The last fundraiser they did earned them the final 
they needed. What percent of the total funds raised did the last fundraiser raise?
The girl's tennis team decided to do multiple fundraisers to raise enough to buy new equipment for next season. The following is a table of 4 of the fundraisers they did and the fraction of the total funds each raised.
The last fundraiser they did earned them the final
The question asks to find what percent the last fundraiser makes up of the total funds raised. The information that's given is how much that last fundraiser made and what fraction the other fundraisers made.
This problem may be solved without the amount of money the last fundraiser raised. The reason is that we know that only 5 fundraisers were done. We're given what the fraction of the other fundraisers were.
If we were to add all the fractions together, including the last fundraiser, the sum of all would equal 1.
Fractions are another version of decimals but also another version of percentages. Percentages are essentially a prettier way of showing parts (or fractions) of a whole, which would be 100%. In the case of fractions, this is the same logic, which is why when all the fractions are summed, they equal 1. This 1 represents 100%.
Upon using lowest common denominators, adding the fractions together, and solving for x, x is calculated to be 
We've almost obtained the final answer. Now it's just a matter of converting this fraction into a percent. As mentioned previously, fractions are another version of decimals. Think of decimals as being the middle conversion between fractions and percents. All that needs to be done to a decimal to turn it in to a percent is to multiply it by 100. For instance, .50 becomes 50%. Conversely, .50 is the same as 
in fraction form. Therefore, one half is 50%.
In order to solve for x in percent, the same conversion must be done.
The question asks to find what percent the last fundraiser makes up of the total funds raised. The information that's given is how much that last fundraiser made and what fraction the other fundraisers made.
This problem may be solved without the amount of money the last fundraiser raised. The reason is that we know that only 5 fundraisers were done. We're given what the fraction of the other fundraisers were.
If we were to add all the fractions together, including the last fundraiser, the sum of all would equal 1.
Fractions are another version of decimals but also another version of percentages. Percentages are essentially a prettier way of showing parts (or fractions) of a whole, which would be 100%. In the case of fractions, this is the same logic, which is why when all the fractions are summed, they equal 1. This 1 represents 100%.
Upon using lowest common denominators, adding the fractions together, and solving for x, x is calculated to be
We've almost obtained the final answer. Now it's just a matter of converting this fraction into a percent. As mentioned previously, fractions are another version of decimals. Think of decimals as being the middle conversion between fractions and percents. All that needs to be done to a decimal to turn it in to a percent is to multiply it by 100. For instance, .50 becomes 50%. Conversely, .50 is the same as
In order to solve for x in percent, the same conversion must be done.
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If a dress in a store originally costs 
, what does it cost (in dollars) after a 
discount is applied?
If a dress in a store originally costs
To find 
of 80, 
. Next, subtract 
, for 
as the final answer.
To find
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A chair company produces 5,000 luxury chairs per year. Each chair requires \$200 in wood and other materials to build. It also requires 3 hours of work by a craftsman, who earns \$30 per hour. If the company wants to earn \$3 million dollars in profit this year, how much should each chair cost?
A chair company produces 5,000 luxury chairs per year. Each chair requires \$200 in wood and other materials to build. It also requires 3 hours of work by a craftsman, who earns \$30 per hour. If the company wants to earn \$3 million dollars in profit this year, how much should each chair cost?
Total cost of chair = materials + labor = \$200 + (3 hours) (\$30/hour) = \$290
Total cost for 5000 chairs = \$290 x 5,000 = \$1,450,000
Profit = (5000) x Price per chair – Cost of Chairs
\$3,000,000 = (5000) x Price per chair – \$1,450,000
\$4,450,000 = (5000) x Price per chair
Price per chair = $4,450,000 / 5,000 = $890
Total cost of chair = materials + labor = \$200 + (3 hours) (\$30/hour) = \$290
Total cost for 5000 chairs = \$290 x 5,000 = \$1,450,000
Profit = (5000) x Price per chair – Cost of Chairs
\$3,000,000 = (5000) x Price per chair – \$1,450,000
\$4,450,000 = (5000) x Price per chair
Price per chair = $4,450,000 / 5,000 = $890
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Patrice earns \$75 per day. Ron earns \$350 per week. How many days does Patrice have to work to earn more than what Ron earns in 5 weeks?
Patrice earns \$75 per day. Ron earns \$350 per week. How many days does Patrice have to work to earn more than what Ron earns in 5 weeks?
Find out how much Ron earns in 5 weeks (\$1750). Divide by Patrice’s daily wage (23.3333 days). Patrice needs to work at least 24 days. At 23 days, she will only have earned \$1725, falling \$25 short of Ron’s 5 week earnings.
Find out how much Ron earns in 5 weeks (\$1750). Divide by Patrice’s daily wage (23.3333 days). Patrice needs to work at least 24 days. At 23 days, she will only have earned \$1725, falling \$25 short of Ron’s 5 week earnings.
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Max bought a book for \$10. If he later sold the book at a 25% profit. How much money in total did he receive from the sale of the book?
Max bought a book for \$10. If he later sold the book at a 25% profit. How much money in total did he receive from the sale of the book?
If the book is sold at a profit we know that the sale price is more than what he bought it for. 25% of \$10 is \$2.50. Therefore the sale price is $10 + $2.50 which is \$12.50. It could also be seen as \$10 X 1.25 =\$12.50
If the book is sold at a profit we know that the sale price is more than what he bought it for. 25% of \$10 is \$2.50. Therefore the sale price is $10 + $2.50 which is \$12.50. It could also be seen as \$10 X 1.25 =\$12.50
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A business launches a new product that produces $x in sales its first year. Sales in the second year are double the first, and the third year has sales four times as large as the first year. If 2nd year sales were \$12 million, how much in total sales was produced over the 3 year period?
A business launches a new product that produces $x in sales its first year. Sales in the second year are double the first, and the third year has sales four times as large as the first year. If 2nd year sales were \$12 million, how much in total sales was produced over the 3 year period?
Write out an equation. Total sales = T = x +2x + 4x
If 2x = 12, x = 6
T = 6 + 12 + 24 = \$42 million
Write out an equation. Total sales = T = x +2x + 4x
If 2x = 12, x = 6
T = 6 + 12 + 24 = \$42 million
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A company made 
in sales last year. The company has four employees. Two of the employees earn 
per year, and the other two employees earn 
per year.
In addition to employee salaries, the company also pays 
a month in rent for its office space and 
per month in general expenses.
What was the company's profit last year?
A company made
In addition to employee salaries, the company also pays
What was the company's profit last year?
Annual profit = Total Annual Sales – Total Annual Expenses
Total Annual Sales = \$400,000
Total Annual Expenses = Salaries + Rent + Expenses
2 employees @ \$50,000 = \$100,000
2 employees @ \$70,000 = \$140,000
12 months of rent @ \$5,000 = \$60,000
12 months of expenses @ \$4,000 = \$48,000
Total Annual Expenses = \$348,000
Annual profit = \$400,000– \$348,000 = \$52,000
Annual profit = Total Annual Sales – Total Annual Expenses
Total Annual Sales = \$400,000
Total Annual Expenses = Salaries + Rent + Expenses
2 employees @ \$50,000 = \$100,000
2 employees @ \$70,000 = \$140,000
12 months of rent @ \$5,000 = \$60,000
12 months of expenses @ \$4,000 = \$48,000
Total Annual Expenses = \$348,000
Annual profit = \$400,000– \$348,000 = \$52,000
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Sam was helping his school raise funds to buy books for the library. He bought small paper pads for \$0.75 and sold them for \$2.00. What was the percent mark-up, rounded to the nearest whole number?
Sam was helping his school raise funds to buy books for the library. He bought small paper pads for \$0.75 and sold them for \$2.00. What was the percent mark-up, rounded to the nearest whole number?
$ Mark-Up = $ New Price – $ Original Price
% Mark-Up = $ Mark-Up ÷ $ Original Price
% Mark-Up = (2.00 – 0.75) ÷ 0.75 = 1.67 or 167 %
$ Mark-Up = $ New Price – $ Original Price
% Mark-Up = $ Mark-Up ÷ $ Original Price
% Mark-Up = (2.00 – 0.75) ÷ 0.75 = 1.67 or 167 %
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Jenny has two jobs. The first is an office job salaried at \$52,000 per year, so she makes the same amount of money every week, no matter how many hours she works. The second is a bartending job. She works 6 hours a night, 2 nights a week. She earns \$3.50 per hour plus tips. If she earned \$450 in tips this week, what is the total amount of money she made this week?
Jenny has two jobs. The first is an office job salaried at \$52,000 per year, so she makes the same amount of money every week, no matter how many hours she works. The second is a bartending job. She works 6 hours a night, 2 nights a week. She earns \$3.50 per hour plus tips. If she earned \$450 in tips this week, what is the total amount of money she made this week?
Salaried job:
\$52,000 / year
1 year = 52 weeks
Therefore: \$52,000 / 52 weeks = \$1,000.00 per week
Bartending job:
6 hours x \$3.50 per hour x 2 nights per week = \$42.00
Total Earned = Salaried + Bartending + Tips
= \$1,000.00 + $42.00 + $450 = \$1,492
Salaried job:
\$52,000 / year
1 year = 52 weeks
Therefore: \$52,000 / 52 weeks = \$1,000.00 per week
Bartending job:
6 hours x \$3.50 per hour x 2 nights per week = \$42.00
Total Earned = Salaried + Bartending + Tips
= \$1,000.00 + $42.00 + $450 = \$1,492
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Madame buys 5 dozen eggs at 10 cents per egg. She then sells each dozen for 2 dollars. What is her profit margin?
Madame buys 5 dozen eggs at 10 cents per egg. She then sells each dozen for 2 dollars. What is her profit margin?
Profit margin is equal to profit / revenue. She bought the eggs for (5)(12)(0.1) = \$6 total. She is selling the eggs for (5)(2)=\$10 total.
The profit margin is equal to 
or 
Profit margin is equal to profit / revenue. She bought the eggs for (5)(12)(0.1) = \$6 total. She is selling the eggs for (5)(2)=\$10 total.
The profit margin is equal to
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A jewelry designer bought a booth at a local craft fair. She paid \$160 for the booth rental for the day. Her necklaces cost \$10 to make and she sells them for \$50 apiece. If she wants to make at least \$1000 profit for the day, how many necklaces must she sell?
A jewelry designer bought a booth at a local craft fair. She paid \$160 for the booth rental for the day. Her necklaces cost \$10 to make and she sells them for \$50 apiece. If she wants to make at least \$1000 profit for the day, how many necklaces must she sell?
Profit on Necklace = Price – Cost = \$50 – \$10 = \$40
Total Profit = # of Necklaces Sold * \$40 – Booth Rental Rate
\$1000 Profit = # of Necklaces * \$40 – $160
$1160 = # of Necklaces * \$40
# Necklaces = 29
Profit on Necklace = Price – Cost = \$50 – \$10 = \$40
Total Profit = # of Necklaces Sold * \$40 – Booth Rental Rate
\$1000 Profit = # of Necklaces * \$40 – $160
$1160 = # of Necklaces * \$40
# Necklaces = 29
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A law firm earned \$2,000,000 this year in fees. If the firm’s annual operating costs are \$1,250,000, what is their profit this year?
A law firm earned \$2,000,000 this year in fees. If the firm’s annual operating costs are \$1,250,000, what is their profit this year?
Profit = Total Fees – Operating Costs = \$2,000,000 – \$1,250,000 = \$750,000
Profit = Total Fees – Operating Costs = \$2,000,000 – \$1,250,000 = \$750,000
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A bakery sells cupcakes for 
per dozen. If it costs 
to make each dozen, how much profit would the bakery earn from selling 
dozen cupcakes?
A bakery sells cupcakes for
The profit that is made is the difference between the amount earned and the amount spent. In this instance, it costs 
to make a dozen cupcakes, but the bakery charges 
per dozen.
To find the profit for one dozen cupcakes:
To find the profit for ten dozen cupcakes:
The profit that is made is the difference between the amount earned and the amount spent. In this instance, it costs
To find the profit for one dozen cupcakes:
To find the profit for ten dozen cupcakes:
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It costs a retail store 
to purchase a bow tie. If this store sells the bow tie for 
, what is its profit percentage? Round to the nearest hundredth.
It costs a retail store
The profit percentage is really just a matter of percent change. We are changing from 
to 
. This is easily computed as:
This is the same as 
!
The profit percentage is really just a matter of percent change. We are changing from
This is the same as
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