# SOLUTION: The sum of the digits of a certain 2-digit number is 13. When you reverse the number, the new number is 9 less than the original number. The difference between the 2 digits is 1. F

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Numbers -> SOLUTION: The sum of the digits of a certain 2-digit number is 13. When you reverse the number, the new number is 9 less than the original number. The difference between the 2 digits is 1. F      Log On

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 Click here to see ALL problems on Numbers Word Problems Question 271141: The sum of the digits of a certain 2-digit number is 13. When you reverse the number, the new number is 9 less than the original number. The difference between the 2 digits is 1. Find the original number.Answer by ankor@dixie-net.com(15746)   (Show Source): You can put this solution on YOUR website!The two digit number: 10x + y : The sum of the digits of a certain 2-digit number is 13. x + y = 13 : When you reverse the number, the new number is 9 less than the original number. 10y + x = 10x + y - 9 10y - y = 10x - x - 9 9y = 9x - 9 simplify, divide by 9 y = x - 1 Find the original number. : replace y in the 1st equation with (x-1) x + (x-1) = 13 2x = 13 + 1 2x = 14 x = 7 then y = 6 : 76 is the number : : Check solution in the statement: "When you reverse the number, the new number is 9 less than the original" 67 = 76 - 9