Linear equations using ratios please help?

Amount of type a is ratio portion of a / ratio portion of sum of all types = number of a / total number

Boys equation: 4/(4+5) = x / 3321

4/9 = x / 3321

x = 3321*4/9 = 1476 = number of boys

Girls equation: 5/(4+5) = y / 3321

y = 5*3321/9 = 1845 = number of girls

To check, add up the numbers. You should get the total

1476+1845 = 3321 {correct}

Another method to check is a bit more cumbersome, but useful

The ration of boys to girls is 4:5

So if you take the number of boys:number of girls and reduce that ratio down, you should get 4:5

1476 : 1845 {reducing a ratio is exactly like reducing a fraction}

4*369 : 5*369

4:5 {correct}

4/5 x 3321 = boys

(3321/9) * 4 = 1476 boys

(3321/9) * 5 = 1845 girls