Question 519069
One of the digits of a two digit number is 6, whose sum is half of their
product, and whose product is half of the reverse order number.  What is
the number?

<pre>
Let t = the tens digit
Let u = the ones or units digit.
</pre>
One of the digits of a two digit number is 6.
<pre>
We aren't told which it is so we have to try both possibilities.

Case 1:  u = 6
</pre>
whose sum is half of their product
<pre>
t + 6 = {{{1/2}}}·6t

t + 6 = 3t

    6 = 2t

    3 = t

So the number is 36
</pre>
and whose product is half of the reverse order number
<pre>
The product is 3*6 = 18 but 18 is not half of the reverse 63.

So Case 1 is eliminated, so it's not 36.

Case 2:  t = 6
</pre>
whose sum is half of their product
<pre>
6 + u = {{{1/2}}}·6u

12 + 2u = 6u

12 = 4u

 3 = u

So the number is 63
</pre>
and whose product of the half of the reverse order number
<pre>
The product is 6*3 = 18 and 18 is indeed half of the reverse 36.

So that's it.  The number is 63.  

Edwin</pre>