Problem 8 · 1992 AJHSME
Medium
Algebra & Patterns
cost-revenue-profit
A store owner bought 1500 pencils at $0.10 each. If he sells them for $0.25 each, how many of them must he sell to make a profit of exactly $100.00?
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Answer: C — 1000.
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Hint 1 of 3
Profit isn't the same as money taken in. Before he earns a single cent of profit, the sales first have to cover what he already spent. How much must come back in before profit even starts?
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Hint 2 of 3
Profit = revenue − cost. Rearranged, the revenue he needs is cost + desired profit — pin that target number first.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you know the dollars he must collect, dividing by the price-per-pencil tells you how many pencils that is.
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Approach: find the revenue target (cost + profit), then divide by price
- He first has to earn back his cost: 1500 × $0.10 = $150. To then clear $100 of profit on top, his sales must total $150 + $100 = $250.
- Each pencil sells for $0.25, so the number sold is $250 ÷ $0.25 = 1000 pencils.
- Why this transfers: in any cost-and-profit problem, money-in must cover money-out before profit begins — so the revenue you aim for is always cost + target profit, never just the profit alone.
- Trap to dodge: answer 400 comes from forgetting the cost ($100 ÷ $0.25); 600 comes from forgetting it the other way. The cost has to be repaid first.
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