Answer: The father is 37 years and the son is 7 years
Step-by-step explanation:
Let x represent the present age of the father.
Let y represent the present age of the son.
Three years hence a father will four times as old as his son will be. This means that
x + 3 = 4(y + 3)
x + 3 = 4y + 12
x - 4y = 12 - 3
x - 4y = 9- - - - - - - - - - - - - - - -1
Before two years he was seven times as old as his son was. This means that
(x - 2) = 7(y - 2)
x - 2 = 7y - 14
x - 7y = - 14 + 2
x - 7y = - 12- - - - - - - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
3y = 21
y = 21.3 = 7
Substituting y = 7 into equation 1, it becomes
x - 4 × 7 = 9
x - 28 = 9
x = 9 + 28
x = 37
