Lets assume that the first boy gets 5x, the second 9x and the third 10x dollars, where x is some number.

The ratio is 5x : 9x : 10x = 5 : 9 : 10.

Also

5x + 9x + 10x = 240

........

click here to see the equation solved for x

........

x = 10

5*10 = $50 is the amount the first boy got.

9*10 = $90 is the amount the second boy got.

10*1- = $100 is the amount the third boy got.