Problem 12 · 2013 AMC 8
Easy
Fractions, Decimals & Percents
percent-savings
At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $50, you get a second pair at a 40% discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $150 regular price did he save?
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Answer: B — 30%.
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Hint 1 of 2
"Percent saved" always means dollars-saved compared to the full regular price ($150 for three pairs), not to what he ended up paying. So you only need the total dollars knocked off.
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Hint 2 of 2
Percent saved = (dollars saved) ÷ (original price). Find the savings in dollars first; the percentages 40% and 50% are just shortcuts to those dollar amounts.
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Approach: total dollars saved ÷ regular price
- Only the 2nd and 3rd pairs are discounted (the 1st is full price). Convert each discount to dollars: 40% of $50 = $20 saved, and half of $50 = $25 saved.
- Total saved = $20 + $25 = $45, against the regular three-pair price of $150.
- Percent saved = 45 ÷ 150 = 30%.
- Watch the trap: the discounts 40% and 50% average to 45%, but each applies to only one of three pairs — spreading the savings over the full $150 is what drops the answer to 30%.
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