SOLUTION: The sum of the digits of a certain two-digits number is 7. When you reverse its digits you increase the number by 27. What is the number.

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Question 1064162: The sum of the digits of a certain two-digits number is 7. When you reverse its digits you increase the number by 27. What is the number.
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(52776) About Me  (Show Source):
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
10a%2Bb= the number
10b%2Ba= the result of reversing the digits
The clues in the problem translate into two equations:
a%2Bb=7= the sum of the digits
%2810b%2Ba%29-%2810a%2Bb%29=27= the reversed number minus the original number
Solving the system:
Simplifying the second equation we get b=a%2B3 :
%2810b%2Ba%29-%2810a%2Bb%29=27
10b%2Ba-10a-b=27
9b-9a=27
9%28b-a%29=27
b-a=27%2F9
b-a=3
b=a%2B3
Substituting a%2B3 for b in a%2Bb=7
we get
a%2Ba%2B3=7
2a%2B3=7
2a=7-3
2a=4
a=4%2F2
a=2
Substituting 2 for a in b=a%2B3 we get
b=2%2B3
b=5
So, the number is highlight%2825%29