Algebra
posted by mike .
w+x=32
y+z=8
w+y=22
x+z=18
220w+300(32w)+400(22w)+180(8y)=9280
,
w+y=22
I was able to solve for w and y but keep coming up with fractions for x and z

The equations do not seem to be independent. #1 and #3, and #2 and #4, when subtracted, both lead to
x  y = 10.
There is probably no unique solution.