ACT Math : How to find the percent of decrease

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Percent Of Decrease

What is the percentage decrease from 2.4 gal. to 3.5 qts.?

 

Possible Answers:

112.53

63.54

33.45

64.53

Correct answer:

63.54

Explanation:

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 %

 

 

 

Example Question #1 : How To Find The Percent Of Decrease

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?

Possible Answers:

21%

7.2%

12.6%

8.4%

11%

Correct answer:

12.6%

Explanation:

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%.

Example Question #14 : Percent Of Change

A local appliance store puts a washing machine that usually sells for $200 on sale for $150.  What is the percent discount?

Possible Answers:

25%

10%

None of the answers are correct

50%

35%

Correct answer:

25%

Explanation:

% 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

Example Question #2 : How To Find The Percent Of Decrease

A company’s annual sales are as follows:

What is the percentage decrease in annual income from and ?

Possible Answers:

 

Correct answer:

Explanation:

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%

Example Question #3 : How To Find The Percent Of Decrease

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?

Possible Answers:

Correct answer:

Explanation:

If the team won  fewer games, subtract  of from :

Step 1: Find % of

Step 2: Subtract from

Example Question #5 : How To Find The Percent Of Decrease

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?

Possible Answers:

Correct answer:

Explanation:

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.

Example Question #4 : How To Find The Percent Of Decrease

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.

Possible Answers:

Correct answer:

Explanation:

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 .

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