During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

Difference between revisions of "2013 AMC 10B Problems/Problem 10"

Problem

A basketball team's players were successful on 50% of their two-point shots and 40% of their three-point shots, which resulted in 54 points. They attempted 50% more two-point shots than three-point shots. How many three-point shots did they attempt?

$\textbf{(A) }10\qquad\textbf{(B) }15\qquad\textbf{(C) }20\qquad\textbf{(D) }25\qquad\textbf{(E) }30$

Solution

Let $x$ be the number of two point shots attempted and $y$ the number of three point shots attempted. Because each two point shot is worth two points and the team made 50% and each three point shot is worth 3 points and the team made 40%, $0.5(2x)+0.4(3y)=54$ or $x+1.2y=54$. Because the team attempted 50% more two point shots then threes, $x=1.5y$. Substituting $1.5y$ for $x$ in the first equation gives $1.5y+1.2y=54$, which equals $2.7y=54$ so $y=$ $\boxed{\textbf{(C) }20}$