SOLUTION: Hello, could you be so, so nice and help me PLEASE??? Thank you so much. Alena When balancing her checkbook, Allison made an error which caused her to show a balance that was $ 5

Question 405996: Hello, could you be so, so nice and help me PLEASE??? Thank you so much.
Alena
When balancing her checkbook, Allison made an error which caused her to show a balance that was $ 54.00 above the actual balance. She had accidently reversed the digits of the amount of one check. The sum of the digits of that check amount was 12.
a) write two equations to represent this situation
b) what is the best method to use to solve this system? Why?
c) solve the equations to determine the true amount of the check.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let x be ten's place, y in units place
The correct check was 10x+y
This was written as 10y=x
..
The error was +54
Original amount - error amount =54

The sum of the digits =12
x+y=12
10x+y-10y+x=54
9x-9y=54.............1
x+y=12..............2
multiply (2) by 9
we get
9x+9y=108
Add it to (1)
18x=162
x= 9
x+y=12
y=3
Actual cheque = 93
error check = 39
difference = 54
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