SOLUTION: In a school, 1200 of the students are boys. If 50% of the boys and 40% of the girls have paid their school fees, find the number of girls, given that 46% of the population has paid

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a school, 1200 of the students are boys. If 50% of the boys and 40% of the girls have paid their school fees, find the number of girls, given that 46% of the population has paid      Log On


   

Question 890584: In a school, 1200 of the students are boys. If 50% of the boys and 40% of the girls have paid their school fees, find the number of girls, given that 46% of the population has paid their school fees.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let b represent the number of boys.
let g represent the nmber of girls.

.5b + .4g = .46(b+g)

that's the equation you need to start with.

now you know that b = 1200, so replace b with 1200 to get:
.5(1200) + .4g = .46(1200+g)

simplify this to get 600 + .4g = 552 + .46g

subtract .4g from both sides of this equation and subtract 552 from both sides of this equation to get:

48 = .06g

solve for g to get:

g = 800

b + g now becomes 1200 + 800 = 2000
.5b + .4g becomes 600 + 320 = 920
920 / 2000 = .46

looks like we're good.

the answer to the question is that there are 800 girls in the school.