Question 970051
The Sum of Two Digits Number is same as its product. find the Number?
Ans is 22 but I dont know how it comes.
<pre>Let number’s tens and units digits be T and U, respectively
Then: T + U = TU
TU – T = U
T(U – 1) = U
{{{T = U/(U - 1)}}}

In order for T to be an integer > 0 in the above equation, U – 1 MUST BE 1. 
We then get: U - 1 = 1
U = 1 + 1, or {{{highlight(U = 2)}}}

We then get: 
{{{T = 2/(2 - 1)}}}, or {{{2/1}}}, or {{{highlight(T = 2)}}}

Therefore, T = 2, and U = 2
Number: {{{highlight_green(22)}}}