SOLUTION: When I am as old as my father is now, I shall 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 mys

Question 205101: When I am as old as my father is now, I shall 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 myself are 100 years. How old is my son?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
When I am as old as my father is now, I shall 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 myself are 100 years. How old is my son?
:
let m = my age now
let s = son's age
let f = father's age
let d = difference between my age and father's age (f - m)
:
From the statement
"When I am as old as my father is now, I shall be five times as old as my son is now."
we can say: (m + d) = 5s = f
or
d = 5s - m
:
" By then, my son will be eight years older than I am now."
s + d = m + 8
replace d with (5s-m)
s + 5s - m = m + 8
6s - 2m = 8
:
" The combined ages of my father and myself are 100 years."
f + m = 100
Replace f with 5s
5s + m = 100
:
How old is my son?
multiply the above equation by 2 and add to; 6s - 2m = 8
10s + 2m = 200
6s - 2m = 8
-------------- eliminates m
16s = 208
s =
s = 13 yrs is my son's age
:
:
:
:
Check solution:
find m:
m + 5s = 100
m + 5(13) = 100
m = 100 - 65
m = 35 yrs is my age
Find the father's age
100 - 35 = 65 is father's age
:
check solution in statement:
"When I am as old as my father is now, I shall be five times as old as my son is now."
65 = 5(13)

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