# SOLUTION: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. what are the two equations?

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 Click here to see ALL problems on Human-and-algebraic-language Question 381751: The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. what are the two equations? Found 2 solutions by ewatrrr, lar:Answer by ewatrrr(10682)   (Show Source): You can put this solution on YOUR website! ``` Hi, Let x and (7-x) represent the original ten and units digits respectively Question states: Reversing its digits increases the number by 9 [10x + (7-x)] + 9 = 10(7 -x) + x Solving for x 9x + 16 = 70 - 9x 18x = 54 x = 3, the original ten's dgit, the original one's digit is 4. (7-3) CHECKING our Answer 34 + 9 = 43 ```Answer by lar(3)   (Show Source): You can put this solution on YOUR website!Let the digits of the number be x and y. So the number is xy (note: this does not mean x times y). x+y=7 and yx=xy+9 In order for yx to equal xy+9, x=y-1. Now we have the two equations x+y=7 and x=y-1. x+y=7 -> x=7-y y-1=7-y 2y=8 y=4 Plug that into one of the original equations: x+4=7 x=3 The number is 34.