Question

The sum of the ages of a father and his two sons is 57 years, and one son is 2 years older then the other. If the elder son lives to be as old as his father is now, and if three are then alive, the sum of their ages will be 162. Find their present ages.

Answer 1

Respuesta:

The present ages are 6, 8 and 43.

Explicación paso a paso:

The age of the father = y

The age of the younger son = x

The age of the older son = x+2

The sum of the three ages = 57

y + x + x + 2 = 57

y + 2x = 57 - 2

y = 55 - 2x

If the elder son lives to be as old as his father is now, the years that have passed are:

y - (x+2) = 55 - 2x - x - 2 = 53 - 3x

Then:

x + (53-3x) + x+2 + (53 - 3x) + y + (53-3x) = 162

x + 53 - 3x + x + 2 + 53 - 3x + 55 - 2x + 53 - 3x = 162

-9x = 162 - 53 - 2 - 53 - 55 - 53

-9x = -54

x = -54/-9 = 6

So:

The younger son is 6 years old.

The elder son is 6+2 = 8 years old

The father is 55-2x = 55-12 = 43 years old

Verification: when the oldest son is 43 years old, 43-8 = 35 years will have elapsed:

41 + 43 + 43 + 35 = 162