Problem 10 · 1995 AJHSME
Hard
Fractions, Decimals & Percents
percent-of-total
A jacket and a shirt originally sold for 80 dollars and 40 dollars, respectively. During a sale Chris bought the 80-dollar jacket at a 40% discount and the 40-dollar shirt at a 55% discount. The total amount saved was what percent of the total of the original prices?
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Answer: A — 45%.
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Hint 1 of 2
The two discount percents (40% and 55%) are taken off DIFFERENT prices, so you can't just average them. Convert each to actual dollars saved first, then compare to the actual total.
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Hint 2 of 2
'What percent of the total' means: (dollars saved) ÷ (total original price), where the total is 80 + 40 = 120.
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Approach: convert percents to dollars, then one percent at the end
- The trap here is averaging 40% and 55% to get 47½% — but those percents sit on different-sized prices, so they don't average. Switch to dollars, where amounts add cleanly.
- Saved on the jacket: 40% of $80 = $32. Saved on the shirt: 55% of $40 = $22. Total saved = $54.
- Original total = $80 + $40 = $120, so the saving is 54120 = 45%.
- Why this transfers: percentages only add or average directly when they're on the same base. Different bases → turn into real quantities first, combine, then take one final percent.
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