SOLUTION: The sum of two digits of a number is 14. If we subtract 29 from the number, then the digits of the number will be equal. Find the number.

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Question 884545: The sum of two digits of a number is 14. If we subtract 29 from the number, then the digits of the number will be equal. Find the number.
Answer by solver91311(24713) (Show Source):
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Let represent the 10s digit and let represent the 1s digit.

We are given that

If we subtract 29 from the number, the 1s digit of the result will be one larger than the 1s digit of the original number and the 10s digit will be 3 smaller (3, not 2 because of the borrow that must occur). Hence we have the relationship: since the digits of the new number must be equal. Rearranging we get:

Solve the 2X2 system to find the two digits of the original number.

John

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