Jasmine Vazquez, who works at a delicatessen, is preparing a...

Jasmine Vazquez, who works at a delicatessen, is preparing a cheese tray using some cheeses that sell for $\$ 8$ per $1 b$ and others that sell for $\$ 12$ per lb. How many pounds of cheese at each price should she use in order for the cheeses on the tray to weigh a total of 56 lb and sell for $\$ 10.50$ per $16 ?$

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Key Concepts

Mixture Problem

A mixture problem involves combining two or more components with different characteristics, such as cost, concentration, or quality, to achieve a mixture that meets specific criteria. In these problems, you typically know the total amount of the mixture and a weighted property, such as the overall price or concentration, which must be met by appropriately mixing the components.

Weighted Average

Weighted average is a method that accounts for the different amounts of components used in a mixture when calculating an overall average value. In the context of blending ingredients, it allows you to determine the target average cost or concentration by considering the proportions and individual values of each component.

Systems of Linear Equations

Systems of linear equations are sets of equations that represent the relationships between variables in a problem. For mixture problems, one equation usually represents the total weight or quantity of the mixture, and another represents the total cost or weighted value, thus allowing the calculation of the individual amounts of each component.

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