Question 710101
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If you are in elementary school mathematics:
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The sum of the digits of a certain two-digit number is 7. 
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So it's either 16, 25, 34, 43, 52, or 61
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Reversing its digits increases the number by 9. what is the number?
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Only 34 fits that bill, since 43 is 9 more than 34.

Answer for elementary school students: 34

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If you are in middle or high school algebra:

t = tens digit
u = units digit
10t+u = the number
10u+t = the number reversed
t+u = the sum of the digits.

</pre>
The sum of the digits of a certain two-digit number is 7. 
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t+u = 7
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Reversing its digits increases the number by 9. what is the number?
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10u+t = (10t+u) + 9

The system to solve is

{{{system(t+u = 7,
10u+t = (10t+u)+9)}}}

Simplify the second equation:

  10u+t = (10t+u)+9

  10u+t = 10t+u+9

  9u-9t = 9

Divide through by 9

    u-t = 1

Solve for u

      u = 1+t

Substitute 1+t for u in

    t+u = 7

t+(1+t) = 7

  t+1+t = 7

   1+2t = 7

Add -1 to both sides

     2t = 6

Divide both sides by 2

     {{{2t/t}}} = {{{6/2}}}

     {{{2cross(t)/cross(t)}}} = {{{cross(6)^3/cross(2)}}}

      t = 3 

Substitute 3 for t in

      u = 1+t

      u = 1+3

      u = 4

Answer for middle school or high school students: 34.

Edwin</pre>