SOLUTION: Sarah blends coffee for Tasti-Delight. She needs to prepare 130 pounds of blended coffee beans selling for $4.73 a pound.She plans to do this by blending together a high-quality be

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Question 224533: Sarah blends coffee for Tasti-Delight. She needs to prepare 130 pounds of blended coffee beans selling for $4.73 a pound.She plans to do this by blending together a high-quality bean costing $5.50 per pound and a cheaper bean at $3.00 per pound. To the nearest pound, find how much high-quality coffee bean she should blend and how much cheaper blend she should blend.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of pounds of coffee at $5.50 per pound, then (130-x) = the number of pounds of coffee at $3.00 per pound. The sum of these two amounts will be 130 pounds of the mixture at $4.73 per pound.
This can be expressed algebraically by:
(5.50)x+(3.00)(130-x) = (130)(4.73) Simplify and solve for x.
5.5x+390-3x = 614.9 Combine like-terms.
2.5x+390 = 614.9 Subtract 390 from both sides.
2.5x = 224.9 Divide both sides by 2.5
x = 89.96 lbs or 90 lbs to the nearest pound.
Sarah will need to blend about 90 pounds of coffee at $5.50 per pound with (130-90 = 40) pounds of coffee at $3.00 per pound to obtain 130 pounds of coffee at $4.73
per pound.