SOLUTION: The sum of the digits of a two-digit number is 6. The number with the digits in reverse order is 6 less than twice the original number. Find the original number.

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Question 921686: The sum of the digits of a two-digit number is 6. The number with the digits in reverse order is 6 less than twice the original number. Find the original number.
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
number: AB

A + B = 6
10B + A = 2(10A + B) - 6

Substitute B = 6 - A into the second equation.

10(6 - A) + A = 2(10A + 6 - A) - 6
60 - 10A + A = 18A + 12 - 6
60 - 9A = 18A + 6
54 = 27A
A = 2 ---> B = 4

The original number is AB = 24.