Question

When the son will be as old as his father today, their ages will add up to 138 years. When the father was as old as the son today, their ages added up to 34 years. Find their present ages

Answer 1

let the difference in their ages be x yrs
let the son's age be y yrs
therefore, (y+x) + (y+x+x) = 138 [i]
and, (y-x) + (y+x-x) = 34 [ii]
[i]: 3x + 2y = 138
[ii]: -x + 2y = 34
[i] + [ii]:
(3x+2y) - (-x+2y) = 138 - 34
3x + x = 104
4x = 104
x = 26
-26 + 2y = 34
2y = 60
y = 30
x + y = 56

therefore the son is 30 years old and the father 56