SOLUTION: If the digits of a two-digit number are interchanged, the result exceeds the original number by 2 more than the sum of the digits. The digits differ by 2. Find the original numbe

That's 10u+t

That means 10u+t = 10t+u PLUS something

Now we're about hear what we are supposed to PLUS onto that

Well, the sum of the digits is t+u, and 2 more
than that is t+u+2.
So we have that 10u+t = 10t+u PLUS t+u+2

or

10u+t = 10t+u + t+u+2

simplify:

10u+t = 11t+2u+2

   8u = 10t+2

Divide through by 2

   4u = 5t+1



The digits differ by 2.  

Oh oh! That doesn't tell us which way to subtract them.

It could be t-u = 2 or u-t = 2

So we have two possible systems of equations:

or

Solve each one by substitution.

One of them comes out t = -9 and u = -11

But that's impossible.  The other one is t=7, u=9

So the number must be 79

Edwin