2013 AMC 10B Problem 10

Question

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?

10

15

20

25

30

Let

x

be the number of three-point attempts

Translate made-shot percentages into total points in terms of

x

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,

so

t=20.

Thus, the correct answer is C.

Problem 10 in other years