Problem 23 · 1988 AJHSME
Stretch
Ratios, Rates & Proportions
profit-per-item
Maria buys computer disks at a price of 4 for $5 and sells them at a price of 3 for $5. How many computer disks must she sell in order to make a profit of $100?
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Answer: D — 240.
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Hint 1 of 2
Profit comes from the gap between what each disk costs her and what each disk earns her. Find that gap for *one* disk, then see how many disks pile up to $100.
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Hint 2 of 2
Cost per disk = $5⁄4; sale price per disk = $5⁄3. Profit per disk is the difference, $5⁄3 − $5⁄4.
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Approach: profit per disk, then scale to $100
- Each disk costs 5⁄4 dollar and sells for 5⁄3 dollar, so the profit per disk is 5⁄3 − 5⁄4 = 20⁄12 − 15⁄12 = 5⁄12 dollar.
- To pile up $100 of profit: 100 ÷ (5⁄12) = 100 × 12⁄5 = 240 disks.
- Why this transfers: profit is always (money in) − (money out) per unit; once you know the profit on one item, any target total is just division by that per-item profit.
Another way — work in whole-disk batches (no fractions):
- Pick a batch size that divides evenly both ways — 12 disks (since 12 is a multiple of 3 and 4). Buying 12 costs 3 groups of $5 = $15; selling 12 brings 4 groups of $5 = $20. So every 12 disks make $20 − $15 = $5 profit.
- $100 ÷ $5 = 20 batches, and 20 × 12 = 240 disks — all whole numbers, no fractions needed.
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