Question 10096
ok, asked to find present ages, so define:


father currently = x
son currently = y

So,
five years ago, father was x-5
five years ago, son was y-5

and,
in 4 years time, father will be x+4
in 4 years time, son will be y+4


Right then, we need 2 equations since we have 2 unknowns:

1. 5 years ago, father was twice as old as son:
--> (x-5) = 2(y-5)
--> x-5 = 2y-10
--> x-2y = -5

2. in 4 years time, sum of ages = 78
--> (x+4) + (y+4) = 78
--> x+y +8 = 78
--> x+y=70


So, now solve the 2 equations:


x-2y = -5
x+y = 70


Subtract them to leave -3y = -75 --> y = 25, so son is now 25.


put this info into one of the 2 equations: pick either. I shall use x+y=70 --> means x must be 70-25, so father is now 45.


NOW, check!

5 years ago, ages were 40 and 20... CORRECT doubled age!
4 years time, ages will be 49 and 29...add together to make 78!


jon.