The Roasted Bean charges 20.00 per pound for Fair Trade...

The Roasted Bean charges 20.00 per pound for Fair Trade Organic Mexican coffee and $18.00$ per pound for Fair Trade Organic Peruvian coffee. How much of each type should be used in order to make a 28-lb blend that sells for 19.00 per pound?

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Key Concepts

Weighted Averages

Weighted averages are used to express the overall property of a mixture by taking into account the contribution of each component relative to its proportion in the blend. The weighted average is computed by multiplying each individual property by its corresponding fraction and then summing these products.

System of Linear Equations

A system of linear equations consists of multiple linear equations that share common variables and must be solved together. In mixture problems, this approach is used to set up relationships between quantities, such as total weight and overall cost, enabling one to determine the values of the unknown amounts in the mixture.

Mixture Problems

A mixture problem involves combining two or more components with different properties to create a blend with a desired overall property. In these problems, one must determine how much of each component is needed based on the total quantity and the target characteristic, such as cost or concentration.

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