2019 AMC 10B Problem 3

Problem 3 of 25EasierAlgebra

In a high school with

500

students,

40\%

of the seniors play a musical instrument, while

30\%

of the non-seniors do not play a musical instrument. In all,

46.8\%

of the students do not play a musical instrument. How many non-seniors play a musical instrument?

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Solution

Let the number of seniors be

s.

Then,

500-s

people aren’t seniors. We know

60\%

of seniors don’t play an instrument. Then, the number of students who don’t play an instrument can be represented as

\begin{aligned} &0.3(500-s)+0.6(s) \\ &= 0.3s+150 \end{aligned}

and

0.468\cdot 500=234.

Thus,

0.3s+150=234

s=280.

This makes the number of non-seniors equal to

220.

Since

70\%

of non-seniors play instruments, we have the total number as

220\cdot 0.7=154.

Thus, the answer is B .