2019 AMC 10B Problems/Problem 3
Contents
Problem
In a high school with students,
of the seniors play a musical instrument, while
of the non-seniors do not play a musical instrument. In all,
of the students do not play a musical instrument. How many non-seniors play a musical instrument?
Solution 1
of seniors do not play a musical instrument. If we denote
as the number of seniors, then
Thus there are non-seniors. Since 70% of the non-seniors play a musical instrument,
.
iron
Solution 2
Let be the number of seniors, and
be the number of non-seniors. Then
Multiplying both sides by gives us
Also, because there are 500 students in total.
Solving this system of equations give us ,
.
Since of the non-seniors play a musical instrument, the answer is simply
of
, which gives us
.
See Also
2019 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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All AMC 10 Problems and Solutions |
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