Problem 15 · 1987 AJHSME
Hard
Algebra & Patterns
solve-linear-equation
The sale ad read: "Buy three tires at the regular price and get the fourth tire for three dollars." Sam paid 240 dollars for a set of four tires at the sale. What was the regular price of one tire?
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Answer: D — 79 dollars.
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Hint 1 of 2
Not all four tires cost the same — one is a flat $3. Peel that special tire off the total before splitting the rest.
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Hint 2 of 2
Of the $240, exactly $3 paid for the fourth tire. The remaining money bought three tires at the same regular price.
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Approach: set the odd-one-out aside first
- The fourth tire was a flat $3, so it accounts for $3 of the $240. That leaves 240 − 3 = 237 dollars covering the three full-price tires.
- Those three are equal, so the regular price is 237 ⁄ 3 = 79 dollars.
- Trap-check: dividing 240 ⁄ 4 = 60 pretends all four tires cost the same — but the $3 tire breaks that. Always remove the unequal piece before averaging the rest.
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