2013 AMC 10A Problem 9

Question

In a recent basketball game, Shenille attempted only three-point shots and two-point shots. She was successful on

20\%

of her three-point shots and

30\%

of her two-point shots. Shenille attempted

30

shots. How many points did she score?

12

18

24

30

36

Let

x

and

y

be the numbers of two-point and three-point attempts

Compare the points earned per attempted shot type after applying the success percentages

Let

x

be the number of two-point shots and

y

be the number of three-point shots.

Then, Shenille makes

0.3x

two-point shots and

0.2y

three-point shots, for a total score of

2 \cdot 0.3x + 3 \cdot 0.2y = 0.6x + 0.6y.

We know that

x + y = 30

0.6(x + y) = 18.

Thus, B is the correct answer.

Problem 9 in other years