Difference between revisions of "2013 AMC 10B Problems/Problem 10"
Richard4912 (talk | contribs) (Blanked the page) |
|||
| Line 1: | Line 1: | ||
| + | ==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? | ||
| + | <math> \textbf{(A) }10\qquad\textbf{(B) }15\qquad\textbf{(C) }20\qquad\textbf{(D) }25\qquad\textbf{(E) }30 </math> | ||
| + | |||
| + | ==Solution== | ||
| + | Call <math>x</math> the number of two point shots attempted and <math>y</math> 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%, <math>0.5(2x)+0.4(3y)=54</math> or <math>x+1.2y=5</math>. Because the team attempted 50% more two point shots then threes, <math>x=1.5y</math>. Substituting <math>1.5y</math> for <math>x</math> in the first equation gives <math>1.5y+1.2y=54</math>, which equals <math>2.7y=54</math> so <math>y=</math> <math>\boxed{\textbf{(C) }20}</math> | ||
Revision as of 19:01, 21 February 2013
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?
Solution
Call 
the number of two point shots attempted and 
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%, 
or 
. Because the team attempted 50% more two point shots then threes, 
. Substituting 
for in the first equation gives 
, which equals 
so 
