2013 AMC 10B Problem 10

Problem 10 of 25EasierAlgebra

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?

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Solution

Let

t

be the number of three-point attempts. The number of made three-point shots is

0.4 t,

giving

1.2t

points. The number of two-point attempts is

1.5t,

so the number made is

0.75t,

giving

1.5t

points. Thus the total number of points satisfies

2.7t=54,

t=20.

Thus, the correct answer is C.