Skip to main content

2011 AMC 12A Problem 6

Problem 6 of 25EasierAlgebra

The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team’s total score was 6161 points. How many free throws did they make?

Answer choices

Show solution

Solution

Let aa be the number of two-point shots. The two-point shots score 2a2a points, and the three-point shots score the same 2a2a points. The free throws number a+1a + 1 and score a+1a + 1 points. The total is 2a+2a+(a+1)=5a+1=61, \begin{aligned} 2a + 2a + (a + 1) \\ = 5a + 1 = 61, \end{aligned} so a=12a = 12 and the free throws number a+1=13.a + 1 = 13. Thus, the correct answer is A.

More practice

Concepts: system of equations · substitution

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.