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Thread: Blending Coffee

  1. #1
    Member harpazo's Avatar
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    Blending Coffee

    A coffee manufacturer wants to market a new blend of coffee that sells for 3 dollars and 90 cents per mixing two coffees that sell for 2 dollars and 75 cents and 5 dollars per pound, respectively. What amount of each coffee should be blended to obtain the desired mixture?

    Hint given in textbook:

    [Assume that the total weight of the desired blend is 100 pounds.]

    My Work:

    Let x = 2 dollars and 75 cents per pound

    Let (100 - x) = pounds at 5 dollars per pound

    My equation is the following:

    x(2.75) + 5(100 - x) = 3.90(100)

    Correct?
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  2. #2
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    Re: Blending Coffee

    Correct.
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  3. #3
    Member harpazo's Avatar
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    Re: Blending Coffee

    x(2.75) + 5(100 - x) = 3.90(100)

    x(2.75) + 500 - 5x = 390

    x(2.75) - 5x = 390 - 500

    -2.25x = -1.10

    x = -1.10/-2.25

    x = 2.0454545455

    Amount of coffee at 2.75 per pound:

    2.75(2.0454545455) = 5.625

    Amount of coffee at 5 dollars per pound:

    100 - 2.0454545455 = 497.9545454545, which we can round off to two decimal numbers to get 497.95.

    Is any of this right?
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  4. #4
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    Re: Blending Coffee

    Quote Originally Posted by harpazo View Post

    x(2.75) - 5x = 390 - 500

    -2.25x = -1.10
    Should be -2.25x = -110 : go stand in the corner!
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  5. #5
    Member harpazo's Avatar
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    Re: Blending Coffee

    I made another typo.

    -2.25x = -110

    x = -110/-2.25

    x = 48.8888888889

    Amount of coffee at 2.75 per pound:

    2.75(48.8888888889) = 134.4444444444, which can then be rounded to be 134.40.

    Amount of coffee at 5 dollars per pound:

    100 - 48.8888888889 = 51.1111111111, which can then be rounded to be 51.10.

    Is any of this right?
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  6. #6
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    Re: Blending Coffee

    Correct.
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  7. #7
    Member harpazo's Avatar
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    Re: Blending Coffee

    Good to know I'm right.
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