Posted by **joy** on Thursday, July 29, 2010 at 10:42am.

The sum of the digits of a two-digit number is 16. If the digits are reversed the new number will be 18 greater than the original number. Find the number.

- math -
**Ms. Sue**, Thursday, July 29, 2010 at 11:31am
By trial and error, I found that three numbers meet the first criteria: 88, 79, 97.

Which of those numbers meets the second criteria?

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**joy**, Thursday, July 29, 2010 at 7:21pm
79

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**tchrwill**, Friday, July 30, 2010 at 5:16pm
Let A = the first digit and B + the second digit.

Then A + B = 16 and 10B + A = 10A + B + 18 or B - A = 2

Adding A + B = 16 and B - A = 2 yields B = 9 and A = 7 making the initial number 79.

Therefore, A + B = 16 and 97 - 79 = 17.

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**tchrwill**, Saturday, July 31, 2010 at 3:12pm
Sorry for the mental error. The hand was slower than the eye.

Let A = the first digit and B + the second digit.

Then A + B = 16 and 10B + A = 10A + B + 18 or B - A = 2

Adding A + B = 16 and B - A = 2 yields B = 9 and A = 7 making the initial number 79.

Therefore, A + B = 16 and 97 - 79 = 18

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