2003 AMC 10A Problem 2

Below is the professionally curated solution for Problem 2 of the 2003 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 10A solutions, or check the answer key.

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Concepts:money ratio and proportion

Difficulty rating: 1050

Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $\$4$ per pair and each T-shirt costs $\$5$ 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 $\$2366,$ how many members are in the League?

$77$

$91$

$143$

$182$

$286$

Solution:

Each T-shirt costs $\$4 + \$5 = \$9.$

Each member needs two pairs of socks and two shirts, costing $2 \cdot 4 + 2 \cdot 9 = \$26.$

The number of members is $2366 \div 26 = 91.$

Thus, the correct answer is B.

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