SOLUTION: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?

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Question 918406: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The number: 10T+U.
Description transcribed: T%2BU=7 and 10U%2BT-%2810T%2BU%29=9.

Be sure you understand that and can work with those equations.


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The "increase by 9" equation:
10U%2BT-10T-U=9
9U-9T=9
highlight_green%28U-T=1%29

Simplified system is now identifiable.
highlight%28system%28U%2BT=7%2CU-T=1%29%29
This system is perfectly ready for solving using the elimination method.

Subtract corresponding members of the equations.
2T=6
T=3
;
Add corresponding members of the equations.
2U=8
U=4
;
The original number is highlight%283%2A10%2B4%2A1=highlight%2834%29%29.