SOLUTION: The age of a man is the same as his wife's age with the digits reversed. The sum of their ages is 99 and the man is 9 years older than his wife. How old is the man?

Question 689712: The age of a man is the same as his wife's age with the digits reversed. The sum of their ages is 99 and the man is 9 years older than his wife. How old is the man?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The age of a man is the same as his wife's age with the digits reversed.
10x + y = man's age
10y + x = wife's age
:
The sum of their ages is 99
10x+y + 10y+x = 99
Combine like terms
11x + 11y = 99
Simplify, divide by 11
x + y = 9
:
the man is 9 years older than his wife.
(10x+y) - (10y+x) = 9
10x - x + y - 10y = 9
9x - 9y = 9
simplify, divide by 9
x - y = 1
:
Using elimination from the two equations
x + y = 9
x - y = 1
---------------adding eliminates y, find x
2x = 10
x = 5
then
5 + y = 9
y = 9 - 5
y = 4
therefore
54 is the man's age
45 is the wife's age

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