# SOLUTION: The sum of the digits of a two-digit number is 9. If the number is doubled, then decreased by 36, the answer is the original number with the digits reversed. Find the number.

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 Click here to see ALL problems on Linear-equations Question 229903: The sum of the digits of a two-digit number is 9. If the number is doubled, then decreased by 36, the answer is the original number with the digits reversed. Find the number. Thanks for helping!!!Found 2 solutions by ankor@dixie-net.com, solver91311:Answer by ankor@dixie-net.com(15649)   (Show Source): You can put this solution on YOUR website!Let the two digit = 10x + y : Write an equation for each statement ; "The sum of the digits of a two-digit number is 9." x + y = 9 or y = (9-x); use this for substitution : " If the number is doubled, then decreased by 36, the answer is the original number with the digits reversed." 2(10x+y) - 36 = 10y + x : 20x = 2y - 36 = 10y + x : 20x - x = 10y - 2y + 36 : 19x = 8y + 36 : Find the number. : Replace y with (9-x) in the above equation, find x: 19x = 8(9-x) + 36 19x = 72 - 8x + 36 19x + 8x = 72 + 36 27x = 108 x = x = 4: I'll let you find y, check solution in the given statement Answer by solver91311(16877)   (Show Source): You can put this solution on YOUR website! Let represent the 10s digit of the original number and let represent the 1s digit. The sum of the digits is 9: The value of the original number: Double the original number: Less 36: The number with the digits reversed: So: Substituting: Solve for and then solve for John