Problem 21 · 1989 AJHSME
Stretch
Fractions, Decimals & Percents
keep-fractionpercent
Jack had a bag of 128 apples. He sold 25% of them to Jill. Next he sold 25% of those remaining to June. Of those apples still in his bag, he gave the shiniest one to his teacher. How many apples did Jack have then?
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Answer: D — 71.
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Hint 1 of 3
Instead of tracking what's sold, track what STAYS: selling 25% means 75% = 3⁄4 remains. That turns each sale into a single multiplication.
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Hint 2 of 3
Each '25% off the remainder' acts on whatever is left at that moment, not on the original — so multiply by 3⁄4 step after step.
Still stuck? Show hint 3 →
Hint 3 of 3
128 was chosen so the 3⁄4's come out whole: 128 → 96 → 72. Then one apple goes to the teacher.
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Approach: keep 3⁄4 each time, then subtract 1
- Reframe each sale by what remains: selling 25% leaves 75% = 3⁄4. After Jill, 128 × 3⁄4 = 96 apples remain.
- The second 25% is taken from the 96 now in the bag, not from the original 128: 96 × 3⁄4 = 72 remain.
- Give the shiniest one to the teacher: 72 − 1 = 71.
- Trap to avoid: the percents do NOT add up to '50% gone.' Each percent eats a slice of a smaller pile, so apply them one at a time, multiplying by 3⁄4 each round — successive percents multiply, they never add.
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