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Math · Original worked example

Find a percent change using the right starting value

Calculate percent decreases and successive discounts with original worked examples. Learn why a percent change uses the original value as its base.

By Raise Your ACT · Updated October 27, 2026 · How we review content

Before you begin

Useful foundation: Convert percentages to decimals and divide two numbers.

Your goal: Distinguish the amount of change from the percent change and identify the base for each percentage.

Percent change is (new value − original value) ÷ original value × 100%. A negative result represents a decrease. For a discount of r written as a decimal, multiply the original price by 1 − r.

Work through an example

A backpack's price falls from $80 to $68. What is the percent decrease?
  1. Find the dollar decrease: $80 − $68 = $12.
  2. Use the original price as the base: 12 ÷ 80 = 0.15.
  3. Convert to a percent: 0.15 × 100% = 15%. The price decreased by 15%.
  4. Check using a multiplier: $80 × (1 − 0.15) = $80 × 0.85 = $68.

Try a question yourself

A $60 jacket is discounted by 20%, then by an additional 10% of the reduced price. What is the final price, before tax?

Choose an answer, then check your reasoning. This public practice is not saved.

Read all answer explanations

$42.00: $42 uses a single 30% discount. The two discounts have different bases, so their percentages cannot simply be added.

$48.00: $48 is the price after only the first discount: $60 × 0.80. Apply the additional 10% to this price.

$43.20 — correct answer: The first discount gives $60 × 0.80 = $48. The second gives $48 × 0.90 = $43.20.

$54.00: $54 applies only a 10% discount to the original $60 and omits the first discount.

What to do next

Practice both increases and decreases. Before calculating, write which amount represents 100% for each step.

Revisit the idea in a week using a different question. Repeating this example can help you understand it, but remembering its answer is not evidence of learning a new problem.

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These original practice examples are independent of ACT and are not official test questions.