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2003 AMC 10A Problem 2

2003 AMC 10A Problem 2AMC 10 Step by Step

Name: Date: September 13, 2026

Linear Equations & Word Problems · difficulty 1 of 5 · about 1 min · position P1-10

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?

A)
$77$
B)
$91$
C)
$143$
D)
$182$
E)
$286$

Answer

Key insight

Each member's kit costs 2(4 + 9) = 26 dollars, so the head count is 2366 divided by 26.

Solution

A T-shirt costs $4 + 5 = 9$ dollars. One member needs two socks-and-shirt sets (home and away), so a member's kit costs
$2 \cdot (4 + 9) = 26 \text{ dollars}.$
If there are $m$ members, then $26m = 2366$ , so $m = 2366 / 26 = 91$ (check: $26 \cdot 91 = 2366$ ).

The answer is $\boxed{\textbf{(B)}\ 91}$ .

Why this works

The total cost is (cost per member) times (number of members). Building the per-member cost carefully, including every item listed, turns the word problem into one division. Read the quantity words ("another pair," "each") before writing anything.

The trap

Using one pair of socks and one shirt per member (13 dollars) and getting 182, choice (D).

Common mistakes

Using one pair of socks and one shirt per member (13 dollars) and getting 182, choice (D).
Taking the shirt to cost $5$ rather than $5$ more than socks, giving $2 \cdot 9 = 18$ per member, which does not divide $2366$ evenly.

Techniques

Set up the equation/formula and compute; no special trick needed