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Free throws made

Source: 2011 AMC A Problem 12

June 25, 2011
algebrasystem of equationsAMC

Problem Statement

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 61 points. How many free throws did they make?
<spanclass=latexbold>(A)</span>13<spanclass=latexbold>(B)</span>14<spanclass=latexbold>(C)</span>15<spanclass=latexbold>(D)</span>16<spanclass=latexbold>(E)</span>17<span class='latex-bold'>(A)</span>\,13 \qquad<span class='latex-bold'>(B)</span>\,14 \qquad<span class='latex-bold'>(C)</span>\,15 \qquad<span class='latex-bold'>(D)</span>\,16 \qquad<span class='latex-bold'>(E)</span>\,17