### All ACT Math Resources

## 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:**

64.53

112.53

63.54

33.45

**Correct answer:**

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 %

### Example Question #2 : 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:**

11%

8.4%

21%

12.6%

7.2%

**Correct answer:**

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%.

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

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

**Possible Answers:**

10%

50%

None of the answers are correct

35%

25%

**Correct answer:**

25%

% 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 #4 : 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:**

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 #5 : 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:**

If the team won fewer games, subtract of from :

Step 1: Find % of

Step 2: Subtract from

### Example Question #6 : 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:**

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 #61 : Percentage

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:**

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 .