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

Answer:

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

Step-by-step 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:

$\dfrac{4.99x+5.99y}{50}=5.93\\\\4.99x+5.99y=296.5$

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.