1967 AHSME Problems/Problem 30
Problem
A dealer bought radios for dollars, a positive integer. He contributed two radios to a community bazaar at half their cost. The rest he sold at a profit of $8 on each radio sold. If the overall profit was $72, then the least possible value of for the given information is:
Solution
The first radios are sold for dollars each, for income of , or simply .
The remaining radios are sold for dollars each, for income of , which expands to .
The amount invested in buying radios for dollars is .
Thus, the total profit is , which simplifies to .
Setting this equal to gives , or .
Since must be an integer, must be a multiple of . If we want to minimize , we want to minimize . Since , setting yields , giving the answer of
See also
1967 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 29 |
Followed by Problem 31 | |
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