Percent of Change - ACT Math
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What is the percentage decrease from 2.4 gal. to 3.5 qts.?
What is the percentage decrease from 2.4 gal. to 3.5 qts.?
Find a common unit – in this case it is ounces. The decrease is from 307.2 oz. to 195.2 oz. (128 oz x 2.4 gal. – 32 oz. x 3.5 qts.) 307.2 oz. – 112 oz. = 195.2 oz. Then, 195.2/307.2 = 63.54 %
Find a common unit – in this case it is ounces. The decrease is from 307.2 oz. to 195.2 oz. (128 oz x 2.4 gal. – 32 oz. x 3.5 qts.) 307.2 oz. – 112 oz. = 195.2 oz. Then, 195.2/307.2 = 63.54 %
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The regular price for a sweater in October is $80. In November, the store holds a Thanksgiving sale, and the price of the sweater is reduced by 7%. In December, the store holds a Christmas sale, and the November price of the sweater is reduced by an additional 6%. At the end of December, Jim purchases the sweater. By what percent did the price of the sweater decrease from October to December?
The regular price for a sweater in October is $80. In November, the store holds a Thanksgiving sale, and the price of the sweater is reduced by 7%. In December, the store holds a Christmas sale, and the November price of the sweater is reduced by an additional 6%. At the end of December, Jim purchases the sweater. By what percent did the price of the sweater decrease from October to December?
In October, the sweater cost $80. In November, it was reduced by 7%. 7% of $80 is $5.60 (0.07 x 80). Thus, the new price of the sweater is $80-$5.60, which is $74.40. In December, the sweater's price is reduced by an additional 6%. 6% of $74.40 is $4.46 (0.06 x 74.40). Thus, the December price for the sweater is $74.40-$4.46, which equals $69.94. To find the percent change, we take the change ($80-$69.94=$10.06) and divide by the initial price ($80). We then multiply that quotient by 100 to get 12.6%.
In October, the sweater cost $80. In November, it was reduced by 7%. 7% of $80 is $5.60 (0.07 x 80). Thus, the new price of the sweater is $80-$5.60, which is $74.40. In December, the sweater's price is reduced by an additional 6%. 6% of $74.40 is $4.46 (0.06 x 74.40). Thus, the December price for the sweater is $74.40-$4.46, which equals $69.94. To find the percent change, we take the change ($80-$69.94=$10.06) and divide by the initial price ($80). We then multiply that quotient by 100 to get 12.6%.
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A local appliance store puts a washing machine that usually sells for $200 on sale for $150. What is the percent discount?
A local appliance store puts a washing machine that usually sells for $200 on sale for $150. What is the percent discount?
% Discount = Amount of Discount ÷ Original Amount
% Discount = (Old Price – New Price) ÷ Original Amount
For this problem we have (200 – 150) ÷ 200 = 0.25 or 25% discount
% Discount = Amount of Discount ÷ Original Amount
% Discount = (Old Price – New Price) ÷ Original Amount
For this problem we have (200 – 150) ÷ 200 = 0.25 or 25% discount
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A company’s annual sales are as follows:
What is the percentage decrease in annual income from 
and 
?
A company’s annual sales are as follows:
What is the percentage decrease in annual income from
2010–2011:
% Decrease = (2010 Income – 2011 Income) / 2010 Income
= (100000 – 94000) / 100000 = 6000 / 100000 = 0.06 = 6%
2011–2012:
% Decrease = (2011 Income – 2012 Income) / 2011 Income
= (94000–93000) / 94000 = 1000 / 94000 = .01 = 1%
2010–2011:
% Decrease = (2010 Income – 2011 Income) / 2010 Income
= (100000 – 94000) / 100000 = 6000 / 100000 = 0.06 = 6%
2011–2012:
% Decrease = (2011 Income – 2012 Income) / 2011 Income
= (94000–93000) / 94000 = 1000 / 94000 = .01 = 1%
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In 2014, a basketball team won 
games. In 2013, the team won 
fewer games than it did in 2014. How many games did the team win in 2013?
In 2014, a basketball team won
If the team won 
fewer games, subtract 
of 
from 
:
Step 1: Find 
% of 
Step 2: Subtract from 
If the team won
Step 1: Find
Step 2: Subtract from
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If a new television cost 
for a store to purchase and was originally on sale for 
, by what percentage must it be marked down in order for the store to make a 
profit?
If a new television cost
First, calculate the amount of profit that will need to be made to earn a 
profit. This is done by converting 
to 
and multiplying it by 
to get 
. This means that the store can mark down the television to 
dollars. Thus, we are asking for the percent change from 
to 
. This is calculated:
This means that it is a 
markdown.
First, calculate the amount of profit that will need to be made to earn a
This means that it is a
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A person who was originally 
pounds lost 
pounds. By what percentage did his or her body weight decrease? Round to the nearest hundredth of a percent.
A person who was originally
The formula for percentage change is represented as:
Since the person has lost 
pounds, he or she will weigh 
. Thus, we know that our formula could be written:
Since we are looking for the percentage of decrease, we can represent this as a positive number. (To decrease by a positive amount is to have a negative percentage change, absolutely speaking.) Thus, our answer is 
.
The formula for percentage change is represented as:
Since the person has lost
Since we are looking for the percentage of decrease, we can represent this as a positive number. (To decrease by a positive amount is to have a negative percentage change, absolutely speaking.) Thus, our answer is
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Truck A has a length of 8'3" (8 ft. and 3 inches). Truck B has a length of 14'5".
What is the percentage increase in length going from Truck A to Truck B?
Truck A has a length of 8'3" (8 ft. and 3 inches). Truck B has a length of 14'5".
What is the percentage increase in length going from Truck A to Truck B?
Find a common unit—in this case it is inches. The increase is from 99” to 173”. To find the percentage increase we find the difference and then divide by the length of Truck A.
or 74.74%
Find a common unit—in this case it is inches. The increase is from 99” to 173”. To find the percentage increase we find the difference and then divide by the length of Truck A.
or 74.74%
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Danielle has two jobs. Her retail job pays her $8.50 per hour and she works 20 hours per week in that job. Her office job pays her $12 per hour and she works 15 hours per week in the office. If she starts working an extra 10 hours a week at her office job, what is her percentage increase in total weekly pay? Round to one decimal point.
Danielle has two jobs. Her retail job pays her $8.50 per hour and she works 20 hours per week in that job. Her office job pays her $12 per hour and she works 15 hours per week in the office. If she starts working an extra 10 hours a week at her office job, what is her percentage increase in total weekly pay? Round to one decimal point.
Pay = Hours worked x Rate per hour
Retail job = 20 x $8.50 = $170.00
Office job = 15 x $12.00 = $180.00
Current weekly pay = $170.00 + $180.00 = $350.00
Additional Office job hours = 10 x $12.00 = $120.00
Percentage Increase = $120 / $350 = .343 (rounded) --> 34.3%
Pay = Hours worked x Rate per hour
Retail job = 20 x $8.50 = $170.00
Office job = 15 x $12.00 = $180.00
Current weekly pay = $170.00 + $180.00 = $350.00
Additional Office job hours = 10 x $12.00 = $120.00
Percentage Increase = $120 / $350 = .343 (rounded) --> 34.3%
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A manager of a pizzeria has five people on his staff. Three are full-time staff, each of whom received a starting salary of $25,000 annually for 40 hours of work per week. Each year they have worked at the pizzeria, their pay increases by 7%. Sally has worked at the pizzeria for one year, Nancy for two years and John for three years. The other two employees are part-time and are paid $8.25 per hour. Irene works 1,000 hours per year and Andrew works 700 hours per year. What is the pizzeria’s cost per year for staff salaries?
A manager of a pizzeria has five people on his staff. Three are full-time staff, each of whom received a starting salary of $25,000 annually for 40 hours of work per week. Each year they have worked at the pizzeria, their pay increases by 7%. Sally has worked at the pizzeria for one year, Nancy for two years and John for three years. The other two employees are part-time and are paid $8.25 per hour. Irene works 1,000 hours per year and Andrew works 700 hours per year. What is the pizzeria’s cost per year for staff salaries?
It is important to remember that the employees who receive an annual increase (Sally, Nancy and John), receive the 7% increase based on the salary from the year before.
If you answered $89,025, you did not account for the 7% increase in salary for Nancy and John.
If you answered $89,525, you did not increase John's salary by 7% for the third year ($26,750 * 7% = $1,872.50 --- $1,872.50 + $26,750 = $28,622.50).
If you answered $91,275, you did not account for the 7% to be applied to John's second year salary; rather, you added the dollar increase ($1750) that he received between his first and second year and added it to his second year salary.
If you answered $93,872.50, you accounted for both part-time employees working 1,000 hours. Therefore, the correct answer is $94,397.50.
It is important to remember that the employees who receive an annual increase (Sally, Nancy and John), receive the 7% increase based on the salary from the year before.
If you answered $89,025, you did not account for the 7% increase in salary for Nancy and John.
If you answered $89,525, you did not increase John's salary by 7% for the third year ($26,750 * 7% = $1,872.50 --- $1,872.50 + $26,750 = $28,622.50).
If you answered $91,275, you did not account for the 7% to be applied to John's second year salary; rather, you added the dollar increase ($1750) that he received between his first and second year and added it to his second year salary.
If you answered $93,872.50, you accounted for both part-time employees working 1,000 hours. Therefore, the correct answer is $94,397.50.
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A fundraiser for a local charity raised $28,000 in donations last year. The fundraiser’s goal for this year is to exceed last year’s donations by 15%. So far, they have raised $31,000. How much more money must the fundraiser raise to reach their goal?
A fundraiser for a local charity raised $28,000 in donations last year. The fundraiser’s goal for this year is to exceed last year’s donations by 15%. So far, they have raised $31,000. How much more money must the fundraiser raise to reach their goal?
First, let's calculate the value of this year's expected goal. Start by calculating 15 percent of last year's goal. Do this by converting 15 percent to a decimal by moving the decimal point two spaces to the left, and then multiplying this number by last year's goal.
Now, we can add this value to last year's goal to obtain the expected goal for this year's fundraiser.
Since $31,000 has been raised so far, the amount remaining is as follows:
First, let's calculate the value of this year's expected goal. Start by calculating 15 percent of last year's goal. Do this by converting 15 percent to a decimal by moving the decimal point two spaces to the left, and then multiplying this number by last year's goal.
Now, we can add this value to last year's goal to obtain the expected goal for this year's fundraiser.
Since $31,000 has been raised so far, the amount remaining is as follows:
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Ben and Sam have a furniture design business. The first year they earn $10,000 in profits. The second year they earn $12,000 in profits. What is the percentage increase in profit between year one and two?
Ben and Sam have a furniture design business. The first year they earn $10,000 in profits. The second year they earn $12,000 in profits. What is the percentage increase in profit between year one and two?
Percentage Increase = (Year Two Profit – Year One Profit) / Year One Profit
= ($12,000 - $10,000) / $10,000 = $2000 / $10,000 = .2 = 20%
Percentage Increase = (Year Two Profit – Year One Profit) / Year One Profit
= ($12,000 - $10,000) / $10,000 = $2000 / $10,000 = .2 = 20%
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A university has 
students currently enrolled in its freshman class. Last year, there were only 
freshman enrolled at the school. By what percentage did the number of students in the freshman class increase?
A university has
To find the percentage increase, use the following formula:
Increased # of students this year / # of students last year
If there were 
students last year, and this year there are 
, the number of students increased by 
. Then, knowing this, you can find what percentage of the original number (
) 
represents.
Therefore:
The number of students increased by 
.
To find the percentage increase, use the following formula:
Increased # of students this year / # of students last year
If there were
Therefore:
The number of students increased by
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What is the percent increase from 
to 
?
What is the percent increase from
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.
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On a given day, the temperature ranges from a low of 
to a high of 
. What is the percent increase of temperature from the day's low to high temperature? Round to the nearest integer.
On a given day, the temperature ranges from a low of
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.
Thus, there was a 
increase in temperature that day.
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.
Thus, there was a
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What is the percent increase from 
of a number to 
of that same number?
What is the percent increase from
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. In this case, don't forget 
:
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. In this case, don't forget
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The price of a particular metal raises from 
to 
. What percent increase did the price see?
The price of a particular metal raises from
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative.
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A particular stock gains 
on its price on Tuesday. On Wednesday, it loses 
of its new price. On Thursday, it gains 
on Wednesday's price. What is the percent increase at the close of business Thursday, compared to the opening price on Tuesday? Do not round until the final answer.
A particular stock gains
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. In this case, to keep our amount constantly compared to Tuesday, set Tuesday's price as a variable.
On Tuesday, gain 20 percent.
On Wednesday, lose 12 percent (thus, multiply by 88 percent).
On Thursday, gain 4 percent.
Thus, our final gain relative to Tuesday is 
.
To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. In this case, to keep our amount constantly compared to Tuesday, set Tuesday's price as a variable.
Thus, our final gain relative to Tuesday is
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Thurman is given 
. Each day, he gains 
on this dollar amount, then loses 
of his total each night. If Thurman gains no other money, what will eventually happen to the total amount of money?
Thurman is given
To find out which option is correct, simply follow one complete cycle (that is to say, one day's worth of actions).
We will use 
to represent the initial amount.
First, increase by 
.
Next, decrease by 
.
So, after each cycle, the total amount of money decreases by 
. Eventually therefore, the money will run out.
To find out which option is correct, simply follow one complete cycle (that is to say, one day's worth of actions).
We will use
So, after each cycle, the total amount of money decreases by
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