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.

A lemonade mixture problem may ask how tartness changes when pure water is added or when different batches of lemonade are combined.

Let’s look down each column and see if there are any relationships we can use.

The column titled “Amount of solution (liters)” does not help because x (20 − x) = 20 resolves to 20 = 20, so it does not help us figure out the value of x.

A typical way to set up a formula for these types of problems is Amount of acid = Percent acidity • Amount of solution.

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We can think about this problem in the same way as we thought about the dry mixture problem.

Let’s use x to represent the amount of 10% solution.

This also means we can use 20 − x to represent the amount of 25% solution, since we know that the total amount of the solution will be 20 liters.

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

We do know the amount of cashews in the mix (8 lbs), but we do not know the amount of walnuts, so we will call that amount a.

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