Question 186120
John reversed the digits in the amount of a check and underpaid a customer by $36. The sum of the digits in the two-digit amount was eight. Find the amount of the check.
:
Let x = 10's digit of the correct amt; 
Let y = units digit
:
10x + y = correct amt
10y + x = incorrect amt
:
Correct# - incorrect# = 36
(10x + y) - (10y + x) = 36
Removed brackets
10x + y - 10y - x = 36
:
9x - 9y = 36
Simplify, divide by 9
x - y = 4
:
Write an equation for the statement,
"sum of the digits in the two-digit amount was eight."
x + y = 8
;
Add the two equations
x - y = 4
x + y = 8
--------------adding eliminates y, find x 
2x = 12
x = 6
then
y = 2, obviously
:
correct $value is 62
incorrect $value  26
------------------------
difference is = 36