SOLUTION: The sum of the digits of a two-digit number is 7. If 9 is subtracted from the number, the answer will be a number with the digits reversed. Find the number.

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Question 371177: The sum of the digits of a two-digit number is 7. If 9 is subtracted from the number, the answer will be a number with the digits reversed. Find the number.
Answer by jvan(28) About Me  (Show Source):
You can put this solution on YOUR website!
This question is a tricky DISABLED_event_one= ] It almost stumped me. You can let the two digit number be xy, with x=the number in the tens digit and y= the number in the ones digit. Now we can write equations using the information from the problem. The sum of the digits is 7: x%2By+=+7. If 9 is subtracted from the number, the answer will be a number with the digits reversed: xy-9=yx. We have found our equations. We move onto the solving part. Now the trick is to add yx to both side of this equation, so xy-9=yx becomes xy%2Byx-9=yx%2Byx. Adding together xy+yx is like adding the x+y (tens digit) and the y+x (ones digit) together. We know from the first equation that x+y=7, so xy+yx=77! So, xy%2Byx-9=yx%2Byx becomes 77-9=yx%2Byx. yx+yx=2yx (because you have two of one thing. The equation then becomes 77-9=2yx, then you get 68=2yx. Divide both sides by 2 to get 34=yx. So, y=3 and x =4. So, the number is 43 (because our number is xy). I hope this helps! Please visit my website at www.myonlinetutor.webs.com to get help with homework problems! =] Thanks!