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14 October, 15:31

HomePride manufactures solid oak racks for displaying baseball equipment and karate belts. They usually sell six times as many baseball racks as karate-belt racks. The net profit is $3 from each baseball rack and $5 from each karate-belt rack. If the company wants a total profit of $46,000, how many of each type of rack should they sell?

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  1. 14 October, 15:53
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    Let the number of baseball racks sold be x.

    Let the number of karate-belt racks sold be y.

    a)

    Since 6 times as many baseball racks is sold as karate-belt racks, we have:

    x = 6y, which is our first equation

    Net profit from baseball racks

    = $3x

    Net profit from karate-belt racks

    = $5y

    Total profit is $46000, so we have:

    3x + 5y = 46000, which is our second equation

    b)

    x = 6y - - - (1)

    3x + 5y = 46000 - - - (2)

    Substituting (1) into (2), we will get:

    3 (6y) + 5y = 46000

    18y + 5y = 46000

    23y = 46000

    y = 46000 / 23

    y = 2000

    Substituting y = 2000 into (1), we will get:

    x = 6 (2000)

    x = 12000

    c)

    They should sell 12000 baseball racks and 2000 karate-belt racks.
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