SOLUTION: Mr. Hughes teaches high school math. He looks young for his age and his students are constantly asking him how old he is. So he told them: “One of the digits of my age is a mult

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Question 835192: Mr. Hughes teaches high school math. He looks young for his
age and his students are constantly asking him how old he is.
So he told them:
“One of the digits of my age is a multiple of the other. The
difference in the digits of my age is half the sum of the digits of
my age.”
How old is Mr. Hughes?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
He is saying that
(1) +t+=+n%2Au+
where +t+ is the tens digit of his age,
+u+ is the units digit of his age, and
+n+ is a whole number
--------------------------
(2) +t+-+u+=+%281%2F2%29%2A%28+t+%2B+u+%29+
Substitute (1) into (2)
(2) +n%2Au+-+u+=+%281%2F2%29%2A%28+n%2Au+%2B+u+%29+
(2) +%28+n-1+%29%2Au+=+%281%2F2%29%2A%28+n%2B1+%29%2Au+
(2) +2u%2A%28+n-1+%29+=+u%2A%28+n%2B1+%29+
(2) +2%2A%28+n-1+%29+=+n+%2B+1+
(2) +2n+-+2+=+n+%2B+1+
(2) +n+=+3+
---------------
(1) +t+=+3u+
+u+ can only be 1,2, or 3 because if +u+=+4+,
then the age exceeds 2 digits
--------------------------
Suppose +u+=+1+ and +t+=+3+
(2) +t+-+u+=+%281%2F2%29%2A%28+t+%2B+u+%29+
(2) +3+-+1+=+%281%2F2%29%2A%28+3+%2B+1+%29+
(2) +2+=+%281%2F2%29%2A4+
(2) +2+=+2+
-------------------
Suppose +u+=+2+ and +t+=+6+
(2) +t+-+u+=+%281%2F2%29%2A%28+t+%2B+u+%29+
(2) +6+-+2+=+%281%2F2%29%2A%28+6+%2B+2+%29+
(2) +4+=+%281%2F2%29%2A8+
(2) +4+=+4+
----------------
Suppose +u+=+3+ and +t+=+9+
That makes him 93 and too old to teach
so, Mr Hughes is either 31 or 62