SECTION A.8 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications A69 3 Solve Mixture Problems Oil refineries sometimes produce gasoline that is a blend of two or more types of fuel; bakeries occasionally blend two or more types of flour for their bread. These problems are referred to as mixture problems because they involve combining two or more quantities to form a mixture. Now Work problem 23 Blending Coffees The manager of a Starbucks store decides to experiment with a new blend of coffee. She will mix some B grade Colombian coffee that sells for $5 per pound with some A grade Arabica coffee that sells for $10 per pound to get 100 pounds of the new blend. The selling price of the new blend is to be $7 per pound, and there is to be no difference in revenue between selling the new blend and selling the other types separately. How many pounds of the B grade Colombian coffee and how many pounds of the A grade Arabica coffees are required? Solution EXAMPLE 4 Let c represent the number of pounds of the B grade Colombian coffee.Then −c 100 equals the number of pounds of the A grade Arabica coffee. See Figure 28. $5 per pound + B Grade Colombian c pounds + $10 per pound = A Grade Arabica 100 - c pounds = $7 per pound Blend 100 pounds Figure 28 c c Revenue from B grade Revenue from A grade Revenue from blend Price per pound ofBgrade Pounds of Bgrade Price per pound ofAgrade Pounds of Agrade Price per pound of blend Pounds of blend $5 $10 100 $7 100 { } { } { } { } { }{ } ( ) + = + = ⋅ + ⋅ − = ⋅ Now solve the equation: ( ) + − = + − = − = − = c c c c c c 5 10 100 700 5 1000 10 700 5 300 60 The manager should blend 60 pounds of B grade Colombian coffee with − = 100 60 40 pounds of A grade Arabica coffee to get the desired blend. Check: The 60 pounds of B grade coffee would sell for ⋅ = $5 60 $300, and the 40 pounds of A grade coffee would sell for ⋅ = $10 40 $400. The total revenue, $700, equals the revenue obtained from selling the blend, as desired. Since there is to be no difference in revenue between selling the A and B grades separately and selling the blend, we have
RkJQdWJsaXNoZXIy NjM5ODQ=