mathematics

arah Meeham blends coffee for​ Tasti-Delight. She needs to prepare 120 pounds of blended coffee beans selling for ​$ 4.75 per pound. She plans to do this by blending together a​ high-quality bean costing ​$ 5.25per pound and a cheaper bean at ​$ 3.25 per pound. To the nearest​ pound, find how much​ high-quality coffee bean and how much cheaper coffee bean she should blend.

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  1. h + c = 120 ... 13 h + 13 c = 13 * 120

    5.25 h + 3.25 c = 4.75 * 120
    ... dividing by .25 ... 21 h + 13 c = 19 * 120

    subtracting equations ... 8 h = 6 * 120

    solve for h , then substitute back to find c

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  2. If using x lbs of cheaper coffee, then
    3.25x + 5.25(120-x) = 4.75*120
    x=30, so
    30 lbs cheap, 90 lbs expensive

    makes sense, since 4.75 is much closer to 5.25 than it is to 3.25

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    oobleck

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