Solve Mixture Problems

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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 total cost of walnuts, then, will be 0.8a, as walnuts cost $0.80 per pound.

Now that we have assigned a variable to the amount of walnuts, we can use these existing relationships (and a bit of logic) to figure out how this relates to the total mix.

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

Solve Mixture Problems Bbc Book Report Writing

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.Although the amount of acid in the mixture is not explicitly provided for us in the problem, we can quickly figure it out by multiplying the amount of needed solution (20 liters) times the acidity (20%, or 0.2) to arrive at 4 liters of acid.Now we need to figure out the remaining relationships.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.A typical way to set up a formula for these types of problems is Amount of acid = Percent acidity • Amount of solution.We can think about this problem in the same way as we thought about the dry mixture problem.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.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.

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