SOLUTION: the age of a man is the same as his wife's age with the digits reversed. if the sum of the age is 99 and the man is 9 years older than his wife, how old is he?
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Question 843344: the age of a man is the same as his wife's age with the digits reversed. if the sum of the age is 99 and the man is 9 years older than his wife, how old is he?
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.
Let 10a+b = man's age
let 10b+a = wife's age
if the sum of the age is 99
10a+b + 10b+a = 99
11a + 11b = 99
simplify, divide by 11
a + b = 9
and the man is 9 years older than his wife,
10a+b - 10b+a = 9
9a - 9b = 9
simplify divide by 9
a - b = 1
:
Add the two equations
a + b = 9\
a - b = 1
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2a = 10
a = 5 is the man's 1st digit
then
b = 4 is his 2nd digit
:
He's 54 and wife's 45
