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Algebra Word Problems

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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 -

    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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