SOLUTION: a certain two digit number is equal to 9 times the sum of its digits. If 63 were subtracted from the number, the digits would be reversed. Find the number.

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Question 813830: a certain two digit number is equal to 9 times the sum of its digits. If 63 were subtracted from the number, the digits would be reversed. Find the number.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

two digit number (xy) is equal to 9 times the sum of its digits.****

 10x + y = 9(x+y)  0r   x-8y = 0 ****

If 63 were subtracted from the number, the digits would be reversed.***

 10x + y - 63 = 10y + x  0r  9x -9y = 63  0r  x-y = 7



 x-8y = 0

 x-y = 7    |Subtracting 2nd EQ from 1st EQ

 -7y = -7

   y = 1   and x = 8    (x-y = 7  or  x = y + 7)

Number is 81 

CHECKING our Answer***

 81=+9%281%2B8%29

& 81 - 63 = 18