Age Problem 8 Solution

This is the solution to the algebra  age problem asked by Joshua that read, "A man is 4 years older than his wife and 5 times as old as his son. When the son was born, the age of the wife was six-sevenths that of her husband's age. Find the age of each."
Ok so here we go...

"A man is 4 years older than his wife"
m = w + 4
Now we will subtract 4 from both sides to use this conveniently later ( you will see)
w = (m-4)

"and 5 times as old as his son."
m = 5s

"When the son was born, the age of the wife was six-sevenths that of her husband's age."
w - s = 6/7(m-s)

7(w-s) = 6(m-s) -->
7w - 7s = 6m - 6s --->
7w = 6m - 6s + 7s --->
7w = 6m + s
replace w with (m-4)
7(m-4) = 6m + s
7m - 28 = 6m + s
7m - 6m = s + 28
m = s + 28
replace m with 5s
5s = s + 28
5s - s = 28
4s = 28
s = 7 yrs is the son's age
then
5(7) = 35 yrs is Dad's age
and
35-4 = 31 yrs is Mom's age

Now check work...
"When the son was born, the age of the wife was six-sevenths that of her husband's age."
31 - 7 = 6/7(35 - 7)
24 = 6/7*28
24 = 24;