SOLUTION: THREE-FOURTHS OF THE GYMNASTICS CLASS ARE GIRLS. AFTER TWELVE BOYS JOIN THE CLASS, THE NUMBER OF BOYS AND GIRLS ARE THE SAME. HOW MANY STUDENTS ARE IN THE CLASS NOW? HOW MANY STUDE

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: THREE-FOURTHS OF THE GYMNASTICS CLASS ARE GIRLS. AFTER TWELVE BOYS JOIN THE CLASS, THE NUMBER OF BOYS AND GIRLS ARE THE SAME. HOW MANY STUDENTS ARE IN THE CLASS NOW? HOW MANY STUDE      Log On


   

Question 95505: THREE-FOURTHS OF THE GYMNASTICS CLASS ARE GIRLS. AFTER TWELVE BOYS JOIN THE CLASS, THE NUMBER OF BOYS AND GIRLS ARE THE SAME. HOW MANY STUDENTS ARE IN THE CLASS NOW? HOW MANY STUDENTS ARE IN THE CLASS AFTER THE 12 BOYS JOIN?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=size of class before the 12 boys join
Then x+12 =size of class after the 12 boys join

Now we know that the total number of girls in the class before the 12 boys are added equals the total number of girls in the class after the 12 boys are added. So, we have:
(3/4)x=1/2(x+12) myltiply each term by 4
3x=2(x+12) get rid of parens
3x=2x+24 subtract 2x from both sides
3x-2x=2x-2x+24 collect like terms
x=24-------------------size of class before the 12 boys are added
x+12=24+12=36--------------------------size of class after the 12 boys are added
CK
(3/4)*24=18
18=1/2 of 36

Hope this helps-----ptaylor