SOLUTION: The sum of the digits of a 2-digit number is 8.The number obtained by interchanging the digits exceeds the given number by 18. Find the given number.

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Question 702268: The sum of the digits of a 2-digit number is 8.The number obtained by interchanging the digits exceeds the given number by 18. Find the given number.
Answer by neatmath(302) (Show Source):
You can put this solution on YOUR website!

This is a tricky one, but let's try it:

Let x be the tens digit of the number.

Let y be the ones digit of the number.

Then we have:

Equation 1: given

Equation 2: given

call this Equation 3

Let's use elimination help us solve this system:

Equation 1 multiplied by 9

Now add Equation 1 to Equation 3:

If y=5, it is easy to see that x=3

Thus, our two-digit number is 35.

Check:

???

YES

The tricky part is getting the give Equation 2 correct.

I hope this helps! Keep practicing! :)

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