Problem 14 · 1985 AJHSME
Hard
Fractions, Decimals & Percents
percent-of-fixed-amount
The difference between a 6.5% sales tax and a 6% sales tax on an item priced at $20 before tax is
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Answer: B — $.10.
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Hint 1 of 2
You don't have to compute both taxes and subtract. Both are a percent of the SAME $20, so the difference in dollars is just the difference in rates, applied once. What is 6.5% − 6%?
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Hint 2 of 2
When two percentages act on the same amount, subtract the rates first, then take that single percent of the amount. Here the gap is only 0.5% — half of one percent.
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Approach: take the percent difference of the price
- The two taxes differ by 6.5% − 6% = 0.5%, and both apply to the same $20, so the extra cost is just 0.5% of $20.
- 0.5% = 0.005, and 0.005 × 20 = $0.10.
- Why this transfers: 'percent of the same base' problems collapse to one calculation — combine the rates before multiplying, instead of computing each piece and subtracting. (Sanity check: 1% of $20 is 20¢, so half a percent is 10¢.)
Mark:
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