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Math Help - Systemof linear equations (determinants)- tricky word problem

  1. #1
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    Systemof linear equations (determinants)- tricky word problem

    A mail-order company charges $4 for shipping orders of less than $50, $6 for orders from $50- $200, and $8 for orders over $200. One day the total shipping charges were $2160 for 384 orders. Find the number of orders shipped at each rate if the number of orders under $50 is 12 more than twice the number of orders over $200.

    I know how to do determinants but just having a hard time figuring out the equations I should be using. Any help would be appreciated. Thank you
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  2. #2
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    Re: Systemof linear equations (determinants)- tricky word problem

    Quote Originally Posted by aliciambrissette View Post
    A mail-order company charges $4 for shipping orders of less than $50, $6 for orders from $50- $200, and $8 for orders over $200. One day the total shipping charges were $2160 for 384 orders. Find the number of orders shipped at each rate if the number of orders under $50 is 12 more than twice the number of orders over $200.

    I know how to do determinants but just having a hard time figuring out the equations I should be using. Any help would be appreciated. Thank you
    1. Let x denote the number of the over-200$-orders.

    Then the less-than-50$-orders are (2x + 12)

    and the 50$-to-200$-orders are 384 - (2x + 12) - x = 372 - 3x

    2. The shipping costs sum up to:

    \displaystyle{x \cdot 8 + (372 - 3x) \cdot 6 + (2x + 12) \cdot 4 = 2160}

    3. Solve for x.
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  3. #3
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    Re: Systemof linear equations (determinants)- tricky word problem

    If you need to do it in terms of matrices and determinants: let x be the number of orders greater than $200, y the number of orders between $50 and $200, and z the number of order less than $50. "A mail-order company charges $4 for shipping orders of less than $50, $6 for orders from $50- $200, and $8 for orders over $200. One day the total shipping charges were $2160"
    so 8x+ 6y+ 4z= 2160.

    "on 384 orders": x+ y+ z= 384.

    "the number of orders under $50 is 12 more than twice the number of orders over $200": z= 2x+ 12.

    Your three equations are
    x+ y+ z= 384,
    8x+ 6y+ 4z= 2160, and
    -2x+ 0y+ z= 12.
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