Question 224533
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.