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in a class, 1/8 of he boys and 1/4 of the girls play the piano, and 3 times as many girls as boys play the piano. If there are 100 boys and girls in the class, how many boys play the piano?

Let B be the number of boys in the class.

Let G be the number of girls in the class.

 

(1/4)G = 3(1/8)B           (3 times as many girls as boys play the piano)

B + G = 100                  (there are 100 boys and girls in the class)

Multiplying the top equation by 8, and the 2nd eqn by 2,

2G = 3B

2B + 2G = 200   

Substituting for 2G = 3B, in the 2nd equation just above,

2B + 3B = 200

5B = 200

B = 40    (G = 60)

Number of boys who play the piano is (1/8)B = 5

by Level 11 User (81.5k points)

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