Question

A store owner makes a special blend of coffee from Colombian Supreme costing $4.99/lb and Mocha Java costing $5.99/lb. The mixture sells for $5.93/lb. If this mixture is made in 50.0-lb batches, how many pounds of each type should be used?

Answer 1

The mixture contains 47 lb of Colombian Supreme and 3 lb of Mocha Java.

Explanation:

We are given the following in the question:

Let x be the amount of Colombian supreme and y be the amount of Mocha java in the mixture.

Total amount of mixture = 50 lb

Thus, we can write the equation:

`x + y =50`

Total unit cost of mixture = $5.93/lb

Cost of Colombian Supreme = $4.99/lb

Cost of Mocha Java = $5.99/lb

Thus, we can write the equation:

`(4.99x+5.99y)/(50)=5.93\\\\4.99x+5.99y=296.5`

Solving the two equations by elimination method,

`4.99x+5.99y-4.99(x+y)=296.5-4.99(50)\\y=47\\x = 50-y=3`

Thus, the mixture contains 47 lb of Colombian Supreme and 3 lb of Mocha Java.