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How to Calculate Percent Increase and Decrease on the ACT

Many students find math questions that involve percent increase and percent decrease somewhat confusing. The first step to answering these questions correctly on the ACT is identifying them when they’re presented.

Some common scenarios for percent increase questions are

  • Sales tax added to the price of an item

  • Tipping a server at a restaurant

  • Interest earned on an investment

Some typical situations for percent decrease questions are

  • Money lost on an investment

  • Discount on an item being sold

  • Deduction from a paycheck due to taxes

After you know whether you’re dealing with percent increase or percent decrease, here’s how you handle the calculations:

  • Increase. Calculate a percent increase as 100 percent + the percent. For example, a percent increase of 15 percent is equal to

    image0.png
  • Decrease. Calculate a percent decrease as 100 percent – the percent. For example, calculate a percent decrease of 20 percent as

    image1.png

The following two examples show you how to handle both types of questions from start to finish.

Example 1

Randy bought a small guitar amplifier priced at $165 with a special coupon that gave him a 15-percent discount. About how much did he end up paying for the amp?

(A)    Less than $100

(B)    Between $100 and $120

(C)    Between $120 and $140

(D)    Between $140 and $160

(E)    More than $160

A 15-percent discount is a percent decrease of 15 percent:

image2.png

Use your calculator to find this percentage of the original price of $165:

image3.png

Thus, the correct answer is Choice (D).

You can apply this method for finding percent increase and decrease to many percent problems.

Example 2

Keith’s portfolio is currently worth $10,200, representing a 20-percent increase on his original investment. How much did he originally invest?

(F)    $7,800

(G)    $8,160

(H)    $8,440

(J)    $8,500

(K)    $8,880

A 20-percent increase is calculated as

image4.png

so use the following formula:

image5.png

Change the percent sign to 0.01 and solve:

image6.png

Therefore, the correct answer is Choice (J).

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