All ACT Math Resources
Example Question #13 : Percent Of Change
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 %
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?
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 #15 : 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?
None of the answers are correct
% 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 ?
% Decrease = (2010 Income – 2011 Income) / 2010 Income
= (100000 – 94000) / 100000 = 6000 / 100000 = 0.06 = 6%
% 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?
If the team won fewer games, subtract of from :
Step 1: Find % of
Step 2: Subtract from
Example Question #4 : 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?
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 #5 : 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.
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 .