The key idea
A percent change multiplies: up p% means ×(1+100p), down p% means ×(1−100p). Chain changes by multiplying the factors, and undo a change by dividing by its factor.
The trap
Adding percents that apply to different amounts, or undoing a 20% discount by adding 20%.
Can Desmos do it?
A calculator handles the arithmetic. Choosing the right base for each percent is the skill being tested.
College Board skill: Percentages · Problem-Solving and Data Analysis
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
A price is increased by 27%, and then the new price is decreased by 35%. The final price is what percent less than the original price?
Show the answer
Answer: 17.45Multiply the factors: 1.27×0.65=0.8255. That is 17.45% less than the original, not 8%.
Level 2 · Test level
A jacket is discounted 15%, and then 4% sales tax is added to the discounted price. The final cost is $97.24. What was the original price of the jacket, in dollars?
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Answer: 110The final cost is the original price times 0.85×1.04=0.884. So the original price is 0.88497.24=110.
Level 3 · Beyond the test
The population of town A is 25% greater than the population of town B. The population of town B is what percent less than the population of town A?
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Answer: 20If B has 100 people, A has 125. B is 25 less than A, and as a percent of A that is 12525×100=20. It isn't 25%, because the base is now A.
Practice all 36 questions
Answer in the drill to get instant feedback, climb the levels, and feed your misses into Tailored practice. Free, no account.
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