SOLUTION: The sum of the digits in a two digit number is 12. The new number obtained when the digits are reversed is 36 more than the original number. Find the original number. (Help, please

First, a little background, so you can understand what's going on:

Two digit numbers are always equal to 

10 times their first digit plus their second digit.

For instance,

23 has first digit 2 and second digit 3.  (10 times 2) plus 3 = 20+3 = 23

74 has first digit 7 and second digit 4.  (10 times 7) plus 4 = 70+4 = 74

11 has first digit 1 and second digit 1.  (10 times 1) plus 1 = 10+1 = 11

So in general:

"FS" has first digit F and second digit S.  (10 times F) plus S = 10F+S  

If you swap the dgits from "FS" to "SF",

"SF" has first digit S and second digit F.  (10 times S) plus F = 10S+F  

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Now for the problem:

Let F = first digit and S = second digit. 

So the number = 10F + S

When you swap (reverse) the digits, the new number is 10S + F 

So the first equation is this: 

F + S = 12

So

  

So the second equation is

  

Let's simplify that:



and simplify it further by dividing through by 9




So you have this system of equations:



Using the second equation, substitute F+4 for S in the 
first equation F+S = 12

F+(F+4) = 12
  F+F+4 = 12
   2F+4 = 12
     2F = 8
      F = 4

Substitute 4 for F in S=F+4

S=4+4
S=8

So the first digit F is 4 and the second digit S is 8

So the number is 48.

Now let's check:

That checks because 4+8 = 12

That checks because 84 is 36 more than 48, because when 36 more than
48 is 48+36 = 84.

So 48 is the correct answer.

[Your teacher probably uses t and u instead of F and S, and says 
"tens digit" instead of "First digit" and "ones or units digit" instead 
of second digit.]

Edwin