Problema Solution

a man has two children, a boy and a girl. The boy is 6 years older than the girl. Two years ago the father's age was three times the sum of the children's ages. In eight years the father's age will be ten years greater than the sum of the children's ages. Find the present ages of the man, boy, and girl.

Answer provided by our tutors

Let x be the current age of boy , y be the age of girl and z be the fathers age

given that x = 6 + y  ==> x  - y = 6

z-2 = 3  * ( x-2 + y -2) ==> 3x+ 3y -z = 10

z + 8 = 10 + (x + y +8+8) ==> x + y -z = -18

subtracting eq 2 from 3,

 2x + 2y = 28 => x + y = 14 solving this and first equation, y = 4 

using this in eq 1, x = 10 years

using both, z = 32 years