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, .
~IronicNinja
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 these system of equations give us , .
Since of the non-seniors play a musical instrument, the answer is simply of , which gives us .
Solution 3 (using the answer choices)
We can clearly deduce that of the non-seniors do play an instrument, but, since the total percentage of instrument players is , the non-senior population is quite low. By intuition, we can therefore see that the answer is around or . Testing both of these gives us the answer .
Video Solution
~savannahsolver
See Also
2019 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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