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2003 AMC 10A Problem 2

Problem 2 of 25EasierAlgebra

Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4\$4 per pair and each T-shirt costs $5\$5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366,\$2366, how many members are in the League?

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Solution

Each T-shirt costs $4+$5=$9.\$4 + \$5 = \$9. Each member needs two pairs of socks and two shirts, costing 2⋅4+2⋅9=$26.2 \cdot 4 + 2 \cdot 9 = \$26. The number of members is 2366÷26=91.2366 \div 26 = 91. Thus, the correct answer is B.

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Concepts: money · ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.