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