Solving A Mixture Problem

A lemonade mixture problem may ask how tartness changes when pure water is added or when different batches of lemonade are combined.The way to solve most mixture problems is to treat them like other rate problems—identify variables, create equations, and make tables to organize the information and highlight ways to solve the problem.

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Learning to think of a mixture as a kind of rate is an important step in learning to solve these types of problems. In a similar way, lemon juice, sugar, and water mixed together make lemonade.

Any situation in which two or more different variables are combined to determine a third is a type of rate. The tartness of the drink will depend on the ratio of the quantities mixed together—that is a rate relationship.

The per-pound price of the mixture is determined by the ratio of the two nuts.

Here, our context is total cost—we want a mixture that costs $1.00/pound.

We can relate what we know and what we want to find out about total cost using the equation total cost = price • amount.

The next step in figuring out this problem is to find our unknown quantities.

The first step here is to figure out the context of the problem and then identify the proper formula that relates all of the information.

We have two types of nuts with different per-pound prices being combined into a mixture.

Therefore, the number of pounds of 85¢‐per‐pound coffee must be the remainder of the twenty pounds, or 20 – x.

Now, make a chart for the cost of each type and the total cost.


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