SOLUTION: The value of a two digit number is twice as large as the sum of its digits. if the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find

Algebra ->  Average -> SOLUTION: The value of a two digit number is twice as large as the sum of its digits. if the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find      Log On


   

Question 873916: The value of a two digit number is twice as large as the sum of its digits. if the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find the original number.
Equation & answer please.
Thanks!!
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

let (xy) be the number
10x+y = 2(x+y)
10x+y=2x+2y
8x-y=0.........................(1)
10y+x =5(10x+y)-9
10y+x=50x+5y-9
-49x+5y=-9.......................(2)
8 x -1 y = 0 .............1

-49 x + 5 y = -9 .............2
Eliminate y
multiply (1)by 5
Multiply (2) by 1
40 x -5 y = 0
-49 x + 5 y = -9
Add the two equations
-9 x = -9
/ -9
x = 1
plug value of x in (1)
8 x -1 y = 0
8 -1 y = 0
-1 y = 0 -8
-1 y = -8
y = 8
Number is 18