Question 224664
Write an equation for each statement:
:
"Working together, Joanne, Kent, and Geoff can process 504 orders per day for their business.":
j + k + g = 504
: 
"Kent can process 20 more orders per day than Joanne can process."
k = j + 20

:
"Geoff can process 104 fewer orders per day than Kent and Joanne combined."
g = k + j - 104
we can also write it:
-j - k + g  = -104
:
 Find the number of orders that each person can process per day.
:
Add the 1st and above equation
 j + k + g = 504
-j - k + g = -104
------------------ addition eliminate j and k, find g
2g = 400
g = 200 per day
:
Using the 1st equation, replace g with 200
j + k + 200 = 504
j + k = 504 - 200
j + k = 304
:
Rearrange the 2nd equation and add to the above equation
-j + k = 20
 j + k = 304
---------------- additions eliminates j, find k
2k = 324
k = {{{324/2}}}
k = 162 per day
:
Find j using the 2nd equation, replace k with 162
162 = j + 20
162 -20 = j
j = 142 per day
:
our solutions: Joanne = 142, Kent = 162; Geoff = 200; (per day)
;
:
Check solution using the 1st statement
""Working together, Joanne, Kent, and Geoff can process 504 orders per day"
142 + 162 + 200 = 504