2003 AMC 10A Problems/Problem 2

Problem

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?

$\mathrm{(A) \ } 77\qquad \mathrm{(B) \ } 91\qquad \mathrm{(C) \ } 143\qquad \mathrm{(D) \ } 182\qquad \mathrm{(E) \ } 286$

Solution

Since T-shirts cost $5$ dollars more than a pair of socks, T-shirts cost $5+4=9$ dollars.

Since each member needs $2$ pairs of socks and $2$ T-shirts, the total cost for $1$ member is $2(4+9)=26$ dollars.

Since $2366$ dollars was the cost for the club, and $26$ was the cost per member, the number of members in the League is $\frac{2366}{26}=91 \Rightarrow B$ .

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2003 AMC 10A Problems/Problem 2

Problem

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