Problem 18 · 1997 AJHSME
Hard
Fractions, Decimals & Percents
percent-decrease
Last week small boxes of facial tissue were priced at 4 boxes for $5. This week they are on sale at 5 boxes for $4. The percent decrease in the price per box during the sale was closest to
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Answer: B — About 35%.
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Hint 1 of 2
'4 for $5' versus '5 for $4' looks like a tidy swap, but the percent change isn't 20%. Boil both down to the same fair unit — the price of ONE box — before comparing.
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Hint 2 of 2
Percent decrease = (drop ÷ ORIGINAL) × 100%. The original price is the denominator, not the new price — that's where this trap bites.
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Approach: reduce to per-box price, divide the drop by the original
- Per box, old price = $5 ÷ 4 = $1.25; sale price = $4 ÷ 5 = $0.80.
- Drop = $1.25 − $0.80 = $0.45. Percent decrease = $0.45 ÷ $1.25 = 0.36 = 36%, closest to 35%.
- Trap: dividing the drop by the NEW price ($0.45 ÷ $0.80 ≈ 56%) is wrong — percent change always measures against where you started.
- You'll see it again: to compare two 'X for $Y' deals, always collapse each to a single unit price first.
Mark:
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