SOLUTION: A number consists of two digits whose sum is five. When the digits are reversed, the number is increased by nine. Find the number.

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

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

We know that the sum of the digits is 5, so we get the equation:

We also know that when we reverse the number, it increases by 9. This implies that:



We can isolate Y from this equation:

And replace it in the previous one:

Now solve for X:


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

I hope this helps!
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