A store sells cashews for 5.00 per pound and peanuts for ...

A store sells cashews for $\$ 5.00$ per pound and peanuts for $\$ 1.50$ per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $\$ 3.00$ per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as selling the nuts separately?

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Key Concepts

Revenue Calculation

Revenue calculation involves determining the total income generated by selling products. In the context of mixture problems, equating the revenue from the mixture to the revenue from selling the components separately helps ensure that the correct proportions are used to meet financial objectives.

Linear Equations

Linear equations represent relationships where the rate of change is constant. In problems involving mixtures and revenue, setting up a linear equation based on the known quantities and desired outcomes allows you to solve for the unknown amount of a component.

Weighted Average

Weighted average is used to calculate the average of values that have different weights or significances. In mixture problems, it helps determine the final value (such as a price or concentration) of the mixture by taking into account the quantity of each component.

Mixture Problems

Mixture problems involve combining two or more components with different characteristics (such as cost or concentration) to create a mixture with a target overall property. These types of problems require setting up relationships that balance the contributions of each component with the desired result.

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