SOLUTION: Twice the ones digit of a positive 2 digit integer is 17 greater than the difference. Reversing increases the number by 9.

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Question 1024204: Twice the ones digit of a positive 2 digit integer is 17 greater than the difference. Reversing increases the number by 9.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Initial number, 10t%2Bu.

This is the description translated into a system of equations.
system%282t=17%2Babs%28t-u%29%2C10u%2Bt-%2810t%2Bu%29=9%29

The difference equation becomes 10u%2Bt-10t-u=9
9u-9t=9
highlight_green%28u-t=1%29.

Handling the absolute value equation gives these two possible equations:
system%28t-u%2B17=2t%2Cor%2C-t%2Bu%2B17=2t%29
-
system%28t%2Bu=17%2Cor%2C3t-u=17%29.


Either or both of the results of the absolute value equation may work. Start with the "non-negative" form to remake the system.
system%28u-t=1%2Cu%2Bt=17%29.
-
Add corresponding members...
2u=18
u=9----------which indicates t=8.


Original or initial number should be 89.