Question 890584
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.