Question 72232
<pre>
the sum of the two-digit number is 11.  When the number is reversed, the number is 63 less than the original number.  Find the original number and show work.

What is asked in the problem?
    Find the original number

Given:
The sum of the two-digit number is 11
When the number is reversed, the number is 63 less than the original number

Representation:
   Let t = tens digit
       u = unit digit
      10t + u = the original two-digit number
      10u + t = the reversed two-digit number

Equation:Translate the given sentences to mathematical sentences
     t + u = 11 
     10u + t = (10t + u) - 63   Simplify
     9u - 9t = -63              Divide both sides by 9
      u - t = -7
  
Solve the two equation simultaneously by elimination or substitution.

  I will use elimination method
    t + u = 11
   -t + u = -7
  ____________
       2u = 4     divide 2 both sides
        u = 2

Substitute u = 2, to any of the two equations to find the other variable t.

   t + u = 11, u = 2
   t + 2 = 11
       t = 11 - 2
       t = 9

To find the original number, substitute t = 9 and u = 2
     10t + u = 10(9) + 2
             =  90 + 2
             =  92  -------------->> answer
     
  
If you want to check substitute t = 9 and u = 2 to any of the two equations
then if the two equation are true after substituting, then you're answer 
is correct.

Happy calculating


Rachel