Question

Coffee beans worth $ 10.50 $10.50 per pound are to be mixed with coffee beans worth $ 13.00 $13.00 per pound to make 50 50 pounds of beans worth $ 11.50 $11.50 per pound. How many pounds of each type of coffee bean should be used?

Answer 1

Answer: 30 pounds of coffee beans worth $10.50 per pound was used.

20 pounds of coffee beans worth $13.00 per pound was used.

Explanation:

Let x represent the number of coffee beans worth $10.50 per pound that should be mixed.

Let y represent the number of coffee beans worth $13.00 per pound that should be mixed.

50 pounds of beans worth $11.50 per pound is to be made. The total cost of the mixture would be

50 × 11.5 = 575

This means that

10.5x + 13y = 575 - - - - - - - 1

The total number of pounds of each type of coffee used is 50. This means that

x + y = 50

Substituting x = 50 - y into equation 1, it becomes.

10.5(50 - y) + 13y = 575

525 - 10.5y + 13y = 575

- 10.5y + 13y = 575 - 525

2.5y = 50

y = 50/2.5 = 20

x = 50 - 20= 30