Playground Game

Question

In a 3^rd grade PE class, 3/4 of all of the boys are paired to 4/5 of all of the girls for a game on the playground.  Each pair consists of one girl and one boy. What fraction of the entire class is paired for the game?

Answer 1

B is the number of boys

G is the number of girls

N is the number of students in the class

(3/4)B = (4/5)G and B+G=N

multiplies first equation by 20

15B = 16G

B = (16/15) G <--- please label this equation ALPHA

B+G= N

(16/15)G + G = N <--- substitutes equation ALPHA

(16/15)G + (15/15)G = N <--- G = 1*G = (15/15)G ,per common denominator of 15

(31/15)G = N <--- combines like terms

G = (15/31)N <-- solves for G

then, since B = (16/15)G per equaiton ALPHA

B = (16/15)(15/31)N

= 16/31 N

B and G are now in terms of N...

substitutes into the original first equation

(3/4)B = (4/5)G

(3/4)(16/31)N = (4/5)(15/31)N

(12/31)N = (12/31)N

12/31 of the class plays the game