A value rises from 30 to 36. Find the percent increase.
Incorrect answer: 16.67%
A 25% increase followed by a 25% decrease does not restore the original amount. The second percentage uses a different base: 100 becomes 125, then 93.75.
Using the new value as the percent-change base
Percent change compares a difference with the original amount. A discount amount is also different from the final price.
The correction
20%
The increase is 6; 6/30 × 100% = 20%.
- Find the original and new amounts; subtract to find the size of the change.
- Divide the change by the original amount, not the new amount.
- Convert the decimal to a percent and name its direction. This formula requires a nonzero original amount.
Try the reasoning in another example
A population falls from 80 to 60. Find the percent decrease.
- The decrease is 80 − 60 = 20.
- 20 ÷ 80 = 0.25.
Answer: 25% decrease
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
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