Work backward from a percent: a mental math trick
When to use it: You know the amount after a percent change and want the amount before it.
Worked example
- Say what share of the original you have: 20% off leaves 80%.
- Divide by that share, written as a decimal.
- Never add the percent back on. That uses the wrong base.
After 20% off, a coat costs $96. What was the original price?
- $96 is 80% of the original.
- $96 ÷ 0.8 = $120.
- Check: 20% of $120 is $24, and $120 − $24 = $96.
Answer: $120
Try three
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After 40% off, a kettle costs $108. What was the original price?
Show the answer
$180
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After 10% off, a coat costs $72. What was the original price?
Show the answer
$80
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After 10% off, a lamp costs $216. What was the original price?
Show the answer
$240