Here's the simplest approach I found. First look at the new ratio 17:22 recognize that 17 is a prime number. There're only so many ways to arrive at 17.
3:4 Girls = 17
4:5 boys = 22
3x + 4y = 17--> 3*(3) = 4*(2) = 17.
Now lets try. 4*(3) + 5*(2) = 22. So that adds up.
4*3 = 12 Boys.
3:4 Girls = 17
4:5 boys = 22
3x + 4y = 17--> 3*(3) = 4*(2) = 17.
Now lets try. 4*(3) + 5*(2) = 22. So that adds up.
4*3 = 12 Boys.
