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31 July, 02:37

A coffee manufacturer uses Colombian and Brazilian coffee beans to produce two blends, robust and mild. A pound of the robust blend requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans. A pound of the mild blend requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans. If the company has 1800 ounces of Colombian beans and 760 ounces of Brazilian beans, how many pounds of each type of coffee should the manufacturer make to use all their beans exactly?

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  1. 31 July, 02:47
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    1800ounces of robust blend requires 1350 ounces of Colombian beans and 450 ounces of Brazilian beans

    760ounces of Mild beans requires 285ounces of Colombian beans and 475ounces of Brazilian beans

    the total of Colombian beans needed in both is 1350+285 = 1635 ounce

    the total of Brazilian beans needed is 450+475 = 925 ounce

    Explanation:

    A pound of the robust blend requires 12 ounces of Colombian beans and 4 ounces of Brazilian beans

    Let robust blend be represented as Rb

    Let Colombian beans be represented as Cb

    Let Brazilian beans be represented as Bb

    The ounce is abbreviated oz 1 pound is 16oz

    1 pound of Rb = 12oz of Cb + 4oz of Bb

    16oz of Rb = 12oz of Cb + 4oz of Bb (it is in ratio of 12:4 which is 3:1, meaning Cb is three parts of four while Bb takes one parts of four)

    To make 1800 ounces of Rb

    Divide by 4 = 1800/4 = 450

    Brazilian beans is one part which is 450oz

    Colombian beans is three parts = 3 x 450 = 1350oz

    1800oz of Rb = 1350oz of Cb + 450oz of Bb

    A pound of the mild blend requires 6 ounces of Colombian beans and 10 ounces of Brazilian beans.

    Let mild blend be represented as Mb

    Let Colombian beans be represented as Cb

    Let Brazilian beans be represented as Bb

    The ounce is abbreviated oz 1 pound is 16oz

    1 pound of Rb = 6oz of Cb + 10oz of Bb

    16oz of Rb = 6oz of Cb + 10oz of Bb (it is in ratio of 6:10 which is 3:5, adding 3 and 5 we get 8; meaning Cb is three parts of eight while Bb takes five parts of eight)

    To make 760 ounces of Mb

    Divide by 8 = 760/8 = 95

    Colombian beans is three parts of eight which is 3 x 95 = 285oz

    Brazilian beans is five parts of eight which is 5 x 95 = 475oz

    760oz of Mb = 285oz of Cb + 475oz of Bb

    1800ounces of robust blend requires 1350 ounces of Colombian beans and 450 ounces of Brazilian beans

    760ounces of Mild beans requires 285ounces of Colombian beans and 475ounces of Brazilian beans

    the total of Colombian beans needed in both is 1350+285 = 1635 ounce

    the total of Brazilian beans needed is 450+475 = 925 ounce
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