# Solve Mixture Problems

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.

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.

We can think about this problem in the same way as we thought about the dry mixture problem.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.The total amount of nuts in the mixture will be the number of pounds of walnuts (a) plus the number of pounds of cashews (8), or a 8.And since we know that the price of the mixture will be

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

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.

The total amount of nuts in the mixture will be the number of pounds of walnuts (a) plus the number of pounds of cashews (8), or a 8.

And since we know that the price of the mixture will be \$1.00 per pound, we can figure out the total cost of the mix by multiplying the amount by the price: 1.00(a 8) = a 8.

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We can think about this problem in the same way as we thought about the dry mixture problem.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.The total amount of nuts in the mixture will be the number of pounds of walnuts (a) plus the number of pounds of cashews (8), or a 8.And since we know that the price of the mixture will be \$1.00 per pound, we can figure out the total cost of the mix by multiplying the amount by the price: 1.00(a 8) = a 8.We can set these quantities equal to each other and then solve for a. Combined, that comes to 18 pounds of the mixture for \$18. 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).Since this is our first mixture problem and we aren’t sure we did it right, let’s check the answer. That is indeed a dollar a pound, which is just what we were looking for. Then we recognized an equivalent relationship in the table: the total cost of the mix must equal the combined costs of the individual quantities that make up the mix.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.We calculated that 10 pounds of walnuts (the variable a) plus 8 pounds of cashews would give us a mixture that costs \$1.00/pound. Identifying this fact led us to the equation 0.8a 10 = a 8, which helped us solve for a.That was complicated, but notice that we did not need to use a system of equations to solve this problem.

.00 per pound, we can figure out the total cost of the mix by multiplying the amount by the price: 1.00(a 8) = a 8.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).Since this is our first mixture problem and we aren’t sure we did it right, let’s check the answer. That is indeed a dollar a pound, which is just what we were looking for. Then we recognized an equivalent relationship in the table: the total cost of the mix must equal the combined costs of the individual quantities that make up the mix.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.We calculated that 10 pounds of walnuts (the variable a) plus 8 pounds of cashews would give us a mixture that costs

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

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.

The total amount of nuts in the mixture will be the number of pounds of walnuts (a) plus the number of pounds of cashews (8), or a 8.

And since we know that the price of the mixture will be \$1.00 per pound, we can figure out the total cost of the mix by multiplying the amount by the price: 1.00(a 8) = a 8.

||

We can think about this problem in the same way as we thought about the dry mixture problem.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.The total amount of nuts in the mixture will be the number of pounds of walnuts (a) plus the number of pounds of cashews (8), or a 8.And since we know that the price of the mixture will be \$1.00 per pound, we can figure out the total cost of the mix by multiplying the amount by the price: 1.00(a 8) = a 8.We can set these quantities equal to each other and then solve for a. Combined, that comes to 18 pounds of the mixture for \$18. 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).Since this is our first mixture problem and we aren’t sure we did it right, let’s check the answer. That is indeed a dollar a pound, which is just what we were looking for. Then we recognized an equivalent relationship in the table: the total cost of the mix must equal the combined costs of the individual quantities that make up the mix.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.We calculated that 10 pounds of walnuts (the variable a) plus 8 pounds of cashews would give us a mixture that costs \$1.00/pound. Identifying this fact led us to the equation 0.8a 10 = a 8, which helped us solve for a.That was complicated, but notice that we did not need to use a system of equations to solve this problem.

.00/pound. Identifying this fact led us to the equation 0.8a 10 = a 8, which helped us solve for a.That was complicated, but notice that we did not need to use a system of equations to solve this problem.

## Comments Solve Mixture Problems

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