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

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) (Show Source): You can put this solution on YOUR website!
He is saying that
(1)
where is the tens digit of his age,
is the units digit of his age, and
is a whole number
--------------------------
(2)
Substitute (1) into (2)
(2)
(2)
(2)
(2)
(2)
(2)
---------------
(1)
can only be 1,2, or 3 because if ,
then the age exceeds 2 digits
--------------------------
Suppose and
(2)
(2)
(2)
(2)
-------------------
Suppose and
(2)
(2)
(2)
(2)
----------------
Suppose and
That makes him 93 and too old to teach
so, Mr Hughes is either 31 or 62

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