The sum of the digits of a two digit number is 9. If the digits are reversed, the new number if 63 greater than the original number. How do you find the original number.?

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Answer 1 · 2015-11-08T03:03:16

18

Let #x# be the ones digit
#=># The tens digit is #9 -x #

#10(9 - x) + x + 63= 10x + (9 - x)#

#=> 90 - 10x + x + 63 = 10x + 9 - x#

#=> 153 - 9x = 9x + 9#

#=> 153 - 9 = 18x#

#=> 144 = 18x#
#=> x = 8#

#=> 9 - x = 9 - 8 = 1#

Therefore, the number we are looking for is

#10(1) + 8 = 18#