SOLUTION: 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.

Question 511286: 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.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
:
Write an equation for each statement:
:
"A man is 4 years older than his wife"
m = w + 4
subtract 4 from both sides
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 = (m-s)
multiply both sides by 7
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
:
;
confirm these solutions in the statement:
"When the son was born, the age of the wife was six-sevenths that of her husband's age."
31 - 7 = (35 - 7)
24 = *28
24 = 24;
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