Solve the problem.
-The manager of a coffee shop has one type of coffee that sells for $7 per pound and another type that sells for $14 per pound. The manager wishes to mix 90 pounds of the $14 coffee to get a mixture that will sell for $10 per pound. How many pounds of the $7 coffee should be used?
A)60 lb
B)120 lb
C)105 lb
D)210 lb

Question

Quizplus · Accepted Answer

To achieve a mixture that sells for $10 per pound, we can use the method of weighted averages. Let $ x $ be the pounds of the $7 coffee. The total cost of the $14 coffee is $ 90 \times 14 = 1260 $ dollars. The total cost of the $7 coffee is $ 7x $ dollars. The total weight of the mixture is $ 90 + x $ pounds, and we want this mixture to sell for $10 per pound. So, the equation to represent this situation is $ \frac{1260 + 7x}{90 + x} = 10 $. Solving this equation for $ x $ gives us:$$ 1260 + 7x = 10(90 + x) $$$$ 1260 + 7x = 900 + 10x $$$$ 360 = 3x $$$$ x = 120 $$Therefore, 120 pounds of the $7 coffee should be used.

Solve the Problem. -The Manager of a Coffee Shop Has One Type of One