🇺🇸 AMC 8 ⇄ switch contest
1990 AJHSME

Problem 8

Problem 8 · 1990 AJHSME Medium
Fractions, Decimals & Percents discount-tax

A dress originally priced at 80 dollars was put on sale for 25% off. If 10% tax was added to the sale price, then the total selling price (in dollars) of the dress was

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Answer: D — 66 dollars.
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Hint 1 of 2
Don't reach for percent formulas — turn the percents into the friendly fractions you know. What simple fraction is 25%? What is 10%?
Still stuck? Show hint 2 →
Hint 2 of 2
Do the steps in the order the store does: discount the price first, then charge tax on the *reduced* price (you don't pay tax on money you saved).
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Approach: turn percents into easy fractions, in order
  1. 25% is just 1/4, so 25% off means you keep 3/4. Three-quarters of $80 is 3×$20 = $60 — no calculator needed.
  2. Tax of 10% on $60 is one-tenth of $60 = $6, added on top. So $60 + $6 = $66.
  3. *Heads-up trap:* take the discount *before* the tax, on the lower price. (Here it happens the order wouldn't change the answer, but on many problems it does — always tax what you actually pay.)
  4. *Worth keeping:* swapping 25%→1/4 and 10%→1/10 turns 'percent of' into one-step mental math.
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