Percentage - ACT Math
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We asked 1000 people their preferences of movie genres. 7.5% of those asked preferred horror movies, 35% preferred romantic films, 20% preferred dramas and 37.5% preferred comedies. How many people liked horror films?
We asked 1000 people their preferences of movie genres. 7.5% of those asked preferred horror movies, 35% preferred romantic films, 20% preferred dramas and 37.5% preferred comedies. How many people liked horror films?
People who prefer horror films = 1000 people x 7.5% = 1000 x 0.075 = 75 people
People who prefer horror films = 1000 people x 7.5% = 1000 x 0.075 = 75 people
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There are 20 students in a class. 35 percent of the students in the class are boys. What fraction of the class is girls?
There are 20 students in a class. 35 percent of the students in the class are boys. What fraction of the class is girls?
There are 20 total students in the class. 35% of 20 is 7. There are 7 boys in the class.
girls in the class.
There are 20 total students in the class. 35% of 20 is 7. There are 7 boys in the class.
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Which of the following represents 
as a fraction?
Which of the following represents
To represent a percentage as a fraction, keep the percentage in the numerator and put 
in the denominator.
Therefore:
To represent a percentage as a fraction, keep the percentage in the numerator and put
Therefore:
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Which of the following fractions is equivalent to 
Which of the following fractions is equivalent to
To convert an integer percentage into an improper fraction, set the percentage as a fraction over 
and simplify as far as you can. At that point, simply convert the improper fraction into a mixed fraction.
To convert an integer percentage into an improper fraction, set the percentage as a fraction over
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A politician promises to spend up to 
of his budget on improving roads. Which of the following is closest to the fraction of their budget the politician must devote to road improvement?
A politician promises to spend up to
To convert a decimal percentage into a fraction, first convert it to a decimal:
Now, set ths as a fraction with 
as the denominator (expanding to as many significant digits as you need to line the fraction up):
Now just reduce your fraction!
To convert a decimal percentage into a fraction, first convert it to a decimal:
Now, set ths as a fraction with
Now just reduce your fraction!
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Convert to a fraction: 
Convert to a fraction:
To convert a percentage to a fraction, divide the percentage by 100, then simplify. The presence of a variable does not significantly affect this process.
To convert a percentage to a fraction, divide the percentage by 100, then simplify. The presence of a variable does not significantly affect this process.
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Convert 
to a fraction.
Convert
Divide 14 by 100. Simplifying this fraction will give the reduced fractional form of 
:
Divide 14 by 100. Simplifying this fraction will give the reduced fractional form of
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A stadium holds a total of 13,758 seats. Of that total, 6,732 seats are full with spectators. How many seats, to the nearest percent, are currently full?
A stadium holds a total of 13,758 seats. Of that total, 6,732 seats are full with spectators. How many seats, to the nearest percent, are currently full?
To answer this question, we must find the percentage of the amount of seats filled up within the stadium. To find a percentage, there are two steps.
First, you divide the part of the total number by the total number itself (in this case the amount of seats filled divided by the total number of seats). So, for this data:
The second step is to multiply your answer by 100 so that it will now be represented as a percentage. So for this data:
The question asked us to round our answer to the nearest whole percent. To do this, we round a number up one place if the last digit is a 5, 6, 7, 8, or 9, and we round it down if the last digit is a 1, 2, 3, or 4. Therefore:
So our answer for the amount of seats filled within the stadium is 
.
To answer this question, we must find the percentage of the amount of seats filled up within the stadium. To find a percentage, there are two steps.
First, you divide the part of the total number by the total number itself (in this case the amount of seats filled divided by the total number of seats). So, for this data:
The second step is to multiply your answer by 100 so that it will now be represented as a percentage. So for this data:
The question asked us to round our answer to the nearest whole percent. To do this, we round a number up one place if the last digit is a 5, 6, 7, 8, or 9, and we round it down if the last digit is a 1, 2, 3, or 4. Therefore:
So our answer for the amount of seats filled within the stadium is
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percent of 
percent of the students in a high school take Anglo-Saxon as their first foreign language. What fraction of the students does this represent?
For percentages, remember that the key language is found in the words "is" and "of". "Of" is translated as multiplication, and "is" is translated as equality. Here, we merely need to set up the equation:
Notice carefully, we use 
to represent the 
of the class. It really is a filler. 
is the same as 
. This is the answer.
For percentages, remember that the key language is found in the words "is" and "of". "Of" is translated as multiplication, and "is" is translated as equality. Here, we merely need to set up the equation:
Notice carefully, we use
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If 
percent of 
percent of a group of peanuts was processed in Indiana, what fraction of the original amount of peanuts does this group represent?
If
For percentages, remember that the key language is found in the words "is" and "of". "Of" is translated as multiplication, and "is" is translated as equality. Here, we merely need to set up the equation:
Notice carefully, we use 
to represent the 
of the group of peanuts processed anywhere. It really is a filler. 
is the same as 
. Reduce this by canceling out the common 
: 
.
For percentages, remember that the key language is found in the words "is" and "of". "Of" is translated as multiplication, and "is" is translated as equality. Here, we merely need to set up the equation:
Notice carefully, we use
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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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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 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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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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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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