SOLUTION: A two digit number is 4 times the sum of its digits. If 27 is added to that number its digits are reversed. Find that number.

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Question 390239: A two digit number is 4 times the sum of its digits. If 27 is added to that number its digits are reversed. Find that number.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 2 digit number = 10a+%2B+b
where a and b are the digits
given:
(1) 10a+%2B+b+=+4%2A%28a+%2B+b%29
(2) 10a+%2B+b+%2B+27+=+10b+%2B+a
Note that the number with the digits reversed is 10b+%2B+a
--------------------------
From (1):
10a+%2B+b+=+4a+%2B+4b
6a+=+3b
2a+=+b
From (2):
10a+%2B+b+%2B+27+=+10b+%2B+a
Using substitution:
10a+%2B+2a+%2B+27+=+10%2A2a+%2B+a
12a+%2B+27+=+20a++%2B+a
9a+=+27
a+=+3
and
b+=+2a
b+=+6
The number is 36
check answer:
(1) 10a+%2B+b+=+4%2A%28a+%2B+b%29
10%2A3+%2B+6+=+4%2A%283+%2B+6%29
36+=+4%2A9
36+=+36
OK
(2) 10a+%2B+b+%2B+27+=+10b+%2B+a
10%2A3+%2B+6+%2B+27+=+10%2A6+%2B+3
63+=+60+%2B+3
63+=+63
OK