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 6 solutions by richwmiller, mananth, solver91311, ikleyn, josgarithmetic, greenestamps:
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(16949) About Me  (Show Source):
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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):
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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

Answer by ikleyn(53742) About Me  (Show Source):
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.
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.
~~~~~~~~~~~~~~~~~~~~~~~~~


        The solution in the post by @mananth, giving the answer '43 ' is incorrect,
        as anybody can check by substituting it to the problem.

        I came to bring a correct and accurate solution.


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=12 but x=4 so y=8.

The number is 48.         ANSWER

Solved correctly.



Answer by josgarithmetic(39790) About Me  (Show Source):
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t and u
tens digit and units digit
Find the number, 10t+u.

system%28t%2Bu=12%2C36%2B10t%2Bu=t%2B10u%29

system%28t%2Bu=12%2C9t-9u=-36%29

system%28t%2Bu=12%2Cu-t=4%29

system%28t%2Bu=12%2C-t%2Bu=4%29
If add those, then find u=8; and find from that, t=4.

The requested two digit number, highlight%2848%29



Answer by greenestamps(13325) About Me  (Show Source):
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Here is a quick mental solution you can use if formal algebra is not required, and if the speed of finding the solution is important -- as in a timed competitive exam.

The difference between a 2-digit number and the number with the digits reversed is 9 times the difference of the two digits. Since the difference between the two 2-digit numbers is 36, the difference between the two digits is 36/9 = 4.

So the sum of the two digits is 12 and the difference is 4. Quick mental reasoning shows the digits are 4 and 8.

So the original number is 48 and the number with the digits reversed is 84.

ANSWER: 48