SOLUTION: solve by system of equations. The sum of the digits of a two digit number is 12. If 18 is added to the number, the digits will be reversed. Find the number. please show all yo

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: solve by system of equations. The sum of the digits of a two digit number is 12. If 18 is added to the number, the digits will be reversed. Find the number. please show all yo      Log On

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Question 380475: solve by system of equations.
The sum of the digits of a two digit number is 12. If 18 is added to the number, the digits will be reversed. Find the number.
please show all your work to help me understand

Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
let the number be xy.
x ten's place
y units place
...
x+y = 12......................1
...
10x+y is the number
..
10x+y+18= 10y+x
10x-x+y-10y=-18
9x-9y=-18
/2
x-y =-2........................2
add 1 & 2
2x=12-2
2x=10
/2
x=5
..
x+y =12
so y=7
..
the number is 57
...
m.ananth@hotmail.ca