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2011 AMC 10A Problem 12

Problem 12 of 25IntermediateAlgebra

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?

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Solution

Let xx be the number of successful two-point shots. Then we have that 2x+2x+(x+1)=61, 2x + 2x + (x + 1) = 61, which simplifies to 5x+1=61 5x + 1 = 61 x=12. x = 12. The number of successful free throws is then 12+1=13.12 + 1 = 13. Thus, A is the correct answer.

More practice

Concepts: linear equation

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