At The Old Home Fill'er Up and Keep on a-Truckin' Cafe,...

At The Old Home Fill'er Up and Keep on a-Truckin' Cafe, Mavis mixes two different types of coffee beans to produce a house blend. The first type costs $\$ 3$ per pound and the second costs $\$ 8$ per pound. How much of each type does Mavis use to make 50 pounds of a blend which costs $\$ 6$ per pound?

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Key Concepts

Mixture Problems

Mixture problems involve combining two or more substances with different properties, such as cost or concentration, in order to achieve a mixture with a desired overall characteristic. This type of problem requires setting up relationships between the components and the final mixture using algebraic methods.

Weighted Averages

Weighted averages are used when different components contribute unequally to the overall average. In the context of mixtures, this concept helps determine the combined cost or concentration of the mixture by accounting for both the individual values and the proportions in which the components are used.

System of Linear Equations

Solving mixture problems typically involves setting up a system of linear equations. One equation represents the total quantity of the mixture, while another represents the total cost or another combined attribute. Solving this system allows for the determination of the unknown quantities of each component.

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