🇺🇸 AMC 8 ⇄ switch contest
1998 AJHSME

Problem 9

Problem 9 · 1998 AJHSME Medium
Fractions, Decimals & Percents successive-discount

For a sale, a store owner reduces the price of a $10 scarf by 20%. Later the price is lowered again, this time by one-half of the reduced price. The price is now

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Answer: C — $4.00.
Show hints
Hint 1 of 2
Each markdown acts on the price standing right then, not the original. Take 20% off first, then apply the second cut to whatever's left.
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Hint 2 of 2
Read 'lowered by one-half of the reduced price' carefully: it removes half of the current price, so the price simply gets cut in half.
Show solution
Approach: apply each cut to the current price, in order
  1. Start at $10. A 20% cut keeps 80%, so the price becomes $10 × 0.8 = $8.
  2. The second cut removes one-half of that $8, leaving half: $8 ÷ 2 = $4.00.
  3. Trap to dodge: the cuts stack on the running price, not on the original $10. Tempting wrong answers come from subtracting both 'off the start' (like 20% + 50% off $10). Always discount the price that exists at that moment.
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