algebra

Sarah blends coffee for Tasti-Delight. She needs to prepare 170 lbs of blended coffee beans selling for $3.59 per pound. She plans to do this by blending together a high-quality bean costing $5.00 per pound and a cheaper bean at $2.00 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. Blend:

    X lbs of hi-quality beans.
    Y lbs of cheaper beans.

    Eq1: X + Y = 170 lbs.
    Eq2: 5x + 2y = 3.59*170 = $610.30.
    Multiply Eq1 by -2 and add the Eqs:
    -2x - 2y = -340
    +5x + 2y = 610.3
    Sum: 3x = 270.3,
    X = 90 lbs.

    90 + y = 170,
    Y = 170 - 90 = 80 lbs.

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