SOLUTION: What is an odd two digit number. The difference of the two digits is 5. The difference in the squares of the two digits is 45

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Question 524554: What is an odd two digit number. The difference of the two digits is 5. The difference in the squares of the two digits is 45
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Let represent the larger of the two digits. Let represent the smaller. We know that they have to be different, and therefore there exists a smaller and a larger because the difference is non-zero.

The difference of the digits is 5:



The difference of the squares is 45:



Add to both sides of the first equation:



Substitute for in the second equation:



Expand the binomial and simplify:







Now you know that one of the digits of your two digit number is 2.

Go back to the first equation:





Now you know that your two digit number is either 72 or 27. Only one of these is odd.

John

My calculator said it, I believe it, that settles it
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