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We can set these quantities equal to each other and then solve for a. Combined, that comes to 18 pounds of the mixture for . We figured out the quantity of walnuts in this mixture by creating a table, organizing our existing information, and then assigning a variable, a, to represent a missing quantity (walnuts).
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.
So here’s a quick primer on how to think about this type of a problem: the percentage of acidity tells us how much pure acid is in the solution.
For example, if a solution is 10% acid, one liter of the solution would have 0.1 liters of pure acid.
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.
Mixtures (and mixture problems) are made whenever different types of items are combined to create a third, “mixed” item.
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.
These liquid mixture problems have many applications in the sciences, where finding a solution with a specific concentration of a chemical is often important to experiments.
Dealing with concepts like acidity in liquid mixture problems may be confusing at first because it is hard to visualize how “acidic” something is.