## When I am as old as my father is now, I will be five times as old as my son is now. By then my son will be eight years older than I am now.

Question

When I am as old as my father is now, I will be five times as old as my son is now. By then my son will be eight years older than I am now. The combined ages of my father and me are 100 years. How old is my son?

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Math
2 weeks
2021-09-27T02:54:15+00:00
2021-09-27T02:54:15+00:00 1 Answer
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## Answers ( )

Answer:h = 13

Step-by-step explanation:Let calli my agep my father ageh my son ageThen d = p – i is the difference in age between my father and meFrom problem statement “When I am as old as my father is now, I will be five times as old as my son is now”i + d = 5*h = p (1)And from “By then my son will be eight years older than I am now”h + d = i + 8 (2)Finallyi + p = 100 (3)Solving these equationsFrom equation (1) d = 5*h – iPlugging that value in equation (2)h + ( 5*h – i ) = i + 8 ⇒ h + 5*h – i = i + 8 ⇒ 6*h – 2*i = 8As 5*h = pAnd i + p = 100i + 5*h = 100 i = 100 – 5*h6*h – 2*i = 8 i = ( 6*h – 8 )/2100 – 5*h = ( 6*h – 8 ) /2200 – 10*h = 6*h – 8

208 = 16*h

h = 208/16

h= 13 years old