AMC10 2013 B

AMC10 2013 B · Q10

AMC10 2013 B · Q10. It mainly tests Systems of equations, Arithmetic misc.

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?

一个篮球队的两分球命中率为50%，三分球命中率为40%，总得分54分。他们尝试的两分球比三分球多50%。他们尝试了多少个三分球？

(A) 10 10

(B) 15 15

(D) 25 25

(E) 30 30

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let x denote the number of three-point shots attempted. Then the number of three-point shots made was 0.4x, resulting in 3(0.4x) = 1.2x points. The number of two-point shots attempted was 1.5x, and they were successful on 0.5(1.5x) = 0.75x of them resulting in 2(0.75x) = 1.5x points. The number of points scored was 1.2x + 1.5x = 54, so x = 20.

设尝试三分球个数为$x$。则命中的三分球个数为$0.4x$，得分$3(0.4x) = 1.2x$分。尝试的两分球个数为$1.5x$，命中$0.5(1.5x) = 0.75x$个，得分$2(0.75x) = 1.5x$分。总得分$1.2x + 1.5x = 54$，所以$x = 20$。

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