# SOLUTION: The sum of the digits of a two-digit number is 9. If the digits are reversed, the number is 27 less than the original. Find the original number.

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 Question 179803: The sum of the digits of a two-digit number is 9. If the digits are reversed, the number is 27 less than the original. Find the original number.Answer by ankor@dixie-net.com(15656)   (Show Source): You can put this solution on YOUR website!The sum of the digits of a two-digit number is 9. If the digits are reversed, the number is 27 less than the original. Find the original number. : Let x = the 10's digit Let y = the units digit then 10x + y = the two-digit number : "The sum of the digits of a two-digit number is 9." x + y = 9 y = (9-x) : "If the digits are reversed, the number is 27 less than the original." 10y + x = (10x + y) - 27 10y - y = 10x - x - 27 9y = 9x - 27 Simplify, divide by 9 y = x - 3 Substitute (9-x) for y 9 -x = x - 3 9 + 3 = x + x 12 = 2x x = 6, then obviously y = 3 ; 63 is the original number : Check solution in the statement: "If the digits are reversed, the number is 27 less than the original." 36 = 63 - 27