Posted by **mike** on Saturday, December 19, 2009 at 10:07pm.

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

- Algebra Word Problems -
**drwls**, Saturday, December 19, 2009 at 11:32pm
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.

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