SOLUTION: The digits of a two-digit number are reversed. When both these two-digit numbers are added, the result is 88, and when subtracted, the result is 54. The original two-digit number c

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Question 326352: The digits of a two-digit number are reversed. When both these two-digit numbers are added, the result is 88, and when subtracted, the result is 54. The original two-digit number contains what digits?
Answer by solver91311(24713) About Me  (Show Source):
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Let represent the 10s digit of the original number, then let represent the 1s digit of the original number.

The original number is then , and the number with the digits reversed is , which can be written .

If you add the two numbers you get 88, so which is to say

If you subtract the two numbers you get 54, so which is to say

Add the two equations



hence



and



Original number is 71, reversed digits is 17. 71 plus 17 = 88, 71 minus 17 = 54.

John