The combined ages of jim, his father, and his grandfather equals 137. his grandfather is 70 years older than jim. and jim is 31 years younger than his father.

Define their age

Let Jim be x years old
Jim = x
Father = x + 31              ← Jim is 31 years younger than the father
Grandfather = x + 70     ← Grandfather is 70 years older than Jim


Combined age is 137, find x

x + (x + 31) + (x + 70) = 137
x + x + 31 + x + 70 = 137
3x + 101 = 137
3x = 137 - 101
3x = 36
x = 12


Find their age

Jim = x = 12

Father = x + 31
Father = 12 + 31
Father = 43

Grandfather = x + 70
Grandfather = 12 + 70
Grandfather = 82


Jim = 12 ; Father = 43 ; Grandfather = 82