Question

Barges from ports X and Y went to cities A and B. X sent 32 barges and Y sent 8. City A received 22 barges and B received 18 Shipping costs $220 from X to A, $300 from X to B, $400 from Y to A, and $180 from Y to B $9280 was spent How many barges went where? 21

Answer 1

Define the following new variables:
X to A = w
X to B = x
Y to A = y
Y to B = z

Here is what you know:
w + x = 32
y + z = 8
w + y = 22
x + z = 18

You have four equations in four unknowns, but they are not independent. You need another equation. One that you can write is:
220w + 300x + 400y +180z = 9280
220w + 300(32-w) + 400(22-w) +180(8-y) = 9280
Turn this into an equation for w and y, and combine it with w + y = 22. That wil let you solve for w and y. After that, the others are easy.