Question 256628
Let the age of Kate  =x
Let the age of Brett =y
Given, Kate is three years less than twice as old as her brother Brett.
            x = 2y-3   ...(1)
Also, next year Bretts age will be three fourths Kates age.
           y+1 = (3/4)*(x+1)
           4(y+1) = 3(x+1)
           4y+4 = 3x+3
Put x = 2y-3 in (2).
           4y+4 = 3(2y-3)+3
           4y+4 = 6y-9+3
           4y-6y = -9+3-4
           -2y = -10
           y = -10/(-2)
           y = 5
Substituting in (1),
           x = 2*5-3 = 10-3 = 7
Therefore, the age of Kate  = 7
and the age of Brett        = 5