SOLUTION: In a class of 100, 1/8 of the boys and 1/4 of the girls play piano, and 3 times as many girls as boys play piano. How many boys play piano?

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Question 981639: In a class of 100, 1/8 of the boys and 1/4 of the girls play piano, and 3 times as many girls as boys play piano. How many boys play piano?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = number of girls in class
+100+-+x+ = numbr of boys in class
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given:
(1) +%28+1%2F4+%29%2Ax+=+3%2A%28+1%2F8+%29%2A%28+100+-+x+%29+
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Multiply both sides by +8+
(1) +2x+=+3%2A%28+100+-+x+%29+
(1) +2x+=+300+-+3x+
(1) +5x+=+300+
(1) +x+=+60+
and
+100+-+x+=+100+-+60+
+100+-+x+=+40+
There are 40 boys in the class
+%28+1%2F8+%29%2A40+=+5+
5 boys play piano
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check:
Three times as many girls play piano, so
+3%2A5+=+15+ girls play piano
This is 1/4 of the girls, so there are
+4%2A15+=+60+ girls in the class
OK