SOLUTION: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original      Log On

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Question 7796: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?

Answer by arunpaul(104) About Me  (Show Source):
You can put this solution on YOUR website!
let the two digit number be xy
such that 10x +y =xy
now as per question
x+y = 11 -----eq1
10y +x = 10x+y+9 ------eq2
or 9y-9x=9
multiply eq1 with9
so we have
9x +9y = 99 ----eq3
add eq3 and eq2 we have
9x +9y = 99
9y -9x = 9
---------------
18y = 108
y = 108/18 = 6
so x = 5 ( by substituting the value of y in eq1)
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