A man lived a fourth of his life as a boy, a fifth as a young man, and a third as an adult. Then he spend 13 years in his old age. How old was he when he died?

1 Answer
Jul 7, 2018

See explanation.

Explanation:

If we denote the total time the man lived as xx, we get:

  • as a boy he spent x/4x4 years,

  • as a young man : x/5x5

  • as an adult: x/3x3

  • in his old age: 1313 years.

All the above expressions sum up to the man's total age, so that leads to an equation:

x/4+x/5+x/3+13=xx4+x5+x3+13=x

x-x/4-x/5-x/3=13xx4x5x3=13

(60x-15x-12x-20x)/60=1360x15x12x20x60=13

13/60x=131360x=13

x=60x=60

Answer:

The man lived for 6060 years.