Problem 2 · 2013 AMC 8
Easy
Fractions, Decimals & Percents
percent-of-price
A sign at the fish market says, "50% off, today only: half-pound packages for just $3 per package." What is the regular price for a full pound of fish, in dollars? (Assume that there are no deals for bulk.)
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Answer: D — $12.
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Hint 1 of 2
Two separate doublings are hiding here: a half-pound is half of a pound (one doubling), and a 50%-off price is half of the regular price (another doubling). What happens if you double twice?
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Hint 2 of 2
"50% off" means the sale price is half the original, so to undo it you double. Always ask "what fraction of the original is this?" before reaching for the discount.
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Approach: double once for the full pound, double again to undo 50% off
- $3 buys half a pound, so a full pound at the sale price is 2 × $3 = $6.
- "50% off" means $6 is only half of the regular price, so regular = 2 × $6 = $12.
- Watch the trap: the two halvings (half-pound and half-price) tempt you to answer $6. Doubling twice — ×4 from the $3 — lands you at $12.
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