SOLUTION: The sum of the digits of a two-digit number is 11. If 27 is added to the number, the digits will be reversed. Find the number.

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Question 79170: The sum of the digits of a two-digit number is 11. If 27 is added to the number, the digits will be reversed. Find the number.
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y=11
X=11-Y AND:
10X+Y+27=10Y+X SUBSTITUTING (11-Y) FOR X IN THIS EQUATION WE GET
10(11-Y)+Y+27=10Y+(11-Y)
110-10Y+Y+27=10Y+11-Y
-10Y+Y-10Y+Y=-110-27+11
-18Y=-126
Y=-126/-18
Y=7 ANSWER X+7=11
X=4 ANSWER.
THE ORIGINAL NUMBER IS 47
47+27=74 THE REVERSE OF THE ORIGINAL NUMBER