Question 32011
Hello!
Let's call X to the first digit and Y to the second digit. The two digit number is then written as:

{{{10X + Y}}}

For example, if the digits are 3 and 7 (the number is 37), then the above expression yields:

{{{10*3 + 7 = 37}}}

We know that the sum of the digits is 5, so we get the equation:
{{{X+Y=5}}}
We also know that when we reverse the number, it increases by 9. This implies that:
{{{10Y+X = 10X+Y+9}}}
{{{9Y - 9X = 9}}}
{{{Y - X = 1}}}

We can isolate Y from this equation:
{{{Y = 1 + X}}}
And replace it in the previous one:
{{{X+1+X = 5}}}
Now solve for X:
{{{1+2X = 5}}}
{{{X = 2}}}

Since the sum is 5, then Y must be 3. Therefore, the number is 23.


I hope this helps!
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