SOLUTION: On his birthday last year John said "My age is the sum of the digits of the year in which I was born". How old is John?

Question 829885: On his birthday last year John said "My age is the sum of the digits of the year in which I was born". How old is John?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
On his birthday last year John said
"My age is the sum of the digits of the year in which I was born".
How old is John?
:
Assuming last year was 2013
Assuming the first two digits of the year he was born is 19, their sum = 10
Let a = 3rd digit of the year he was born
Let b = 4th digit of the year he was born
:
2013 - (1900+10a+b) = 1+9+a+b
2013 - 1900 - 10a - b = 10 + a + b
113 - 10a - a - b - b = 10
113 - 11a - 2b = 10
-2b = 11a + 10 - 113
-2b = 11a - 103
Divide both sides by -2
b = -5.5a + 51.5
Only integer solution a=9, b=2
He was born in 1992, sum of the digits 21, which is his age
:
Check this 2013-1992 = 21
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