SOLUTION: The sum of the digits of a two- digit number is 12. If 36 is added to the number, then the number obtained is the original with its digits interchanged. Find the original number.

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Question 279490: The sum of the digits of a two- digit number is 12. If 36 is added to the number, then the number obtained is the original with its digits interchanged. Find the original number.
Found 3 solutions by richwmiller, mananth, solver91311:
Answer by richwmiller(17219) About Me  (Show Source):
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x=10a+b
a+b=12
x+36=10b+a
x=48
check
48+36=84
4+8=12
ok

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the digits of a two- digit number is 12. If 36 is added to the number, then the number obtained is the original with its digits interchanged. Find the original number.
Let x be in the tens place and y in units place
x+y =12
10x+y+36 = 10y+x
10x-10y+y-x+36=0
9x-9y=-36
x+y=12
9x+9y=108
18x=72
x=4
x+y=7 but x=4 so y=3 Number 43


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Let represent the 10s digit. Let represent the 1s digit.

The sum of the digits is 12 so:

The value of the original number must be:



Adding 36



The value of the number with the digits reversed must be:



So:



Which is to say:



Or



Add that last equation to the first equation:







That means must be 12 - 4 = 8 and that makes the original number be 48.

Check 48 plus 36 is 84 which is 48 with the digits reversed.

John