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.

Question

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.

Henry · Answer

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.