SOLUTION: The sum of the digits of a two digit number is seven. When the digits are reversed, the number is increased by 27. Find the number.

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Question 692980:
The sum of the digits of a two digit number is seven. When the digits are reversed, the number is increased by 27. Find the number.
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y=7 OR X=7-Y
10X+Y=10Y+X-27 REPLACE X WITH (7-Y) * SOLVE FOR Y.
10(7-Y)+Y=10Y+(7-Y)-27
70-10Y+Y=10Y+7-Y-27
-10Y-10Y+Y+Y=7-27-70
-18Y=-90
Y=-90/-18
Y=5 ANS FOR THE 10'S DIGIT OF THE ORIGINAL NUMBER.
X+5=7
X=7-5=2 ANS. FOR THE UNITS DIGIT IN THE ORIGINAL NUMBER.
PROOF:
52-25=27
27=27