SOLUTION: John reversed the digits in the ammount 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.

Question 186120This question is from textbook Algebra 1
: John reversed the digits in the ammount 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. This question is from textbook Algebra 1

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
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