Question 554011
The difference between a number consisting of two digits and the number formed by reversing the digits is 45.  
<pre>
There are only 4 such numbers:

61, since 61 - 16 = 45
72, since 72 - 27 = 45
83, since 83 - 38 = 45
94, since 94 - 49 = 45
</pre>
The sum of three times the tens digit and five times the units is 47.  There
are only 2 such numbers:
<pre>
47, since 3*4 + 5*7 = 12 + 35 = 47
94, since 3*9 + 5*4 = 27 + 20 = 47

So the only 2-digit number having both properties is 94.

But your teacher will not accept that method.  

Here's how to work it with algebra:
</pre>
The difference between a number consisting of two digits and the number formed by reversing the digits is 45.
<pre>
(10t + u) - (10u + t) = 45

Simplify:

    10t + u - 10u - t = 45

Collect like terms:

              9t - 9u = 45

Divide through by 9:

                t - u = 5 
</pre>
The sum of three times the tens digit and five times the units is 47.
<pre>
              3t + 5u = 47

Solve the system of equations:

               t -  u =  5
              3t + 5u = 47

Solve the first for t:

                t - u =  5
                    t = 5 + u

Substitute in 

              3t + 5u = 47
        3(5 + u) + 5u = 47
         15 + 3u + 5u = 47
                   8u = 32 
                    u = 4

Substitute in

                    t = 5 + u  
                    t = 5 + 4
                    t = 9

number = 10t + u = 10(9) + 4 = 94 

Edwin</pre>