Solving A Mixture Problem

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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.

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.

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.

These problems arise in many settings, such as when combining solutions in a chemistry lab or adding ingredients to a recipe.

Mixtures (and mixture problems) are made whenever different types of items are combined to create a third, “mixed” item.

Coffee worth

Mixtures (and mixture problems) are made whenever different types of items are combined to create a third, “mixed” item.

Coffee worth $1.05 per pound is mixed with coffee worth 85¢ per pound to obtain 20 pounds of a mixture worth 90¢ per pound. First, circle what you are trying to find— how many pounds of each type.

Now, let the number of pounds of $1.05 coffee be denoted as x.

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.

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Mixtures (and mixture problems) are made whenever different types of items are combined to create a third, “mixed” item.Coffee worth $1.05 per pound is mixed with coffee worth 85¢ per pound to obtain 20 pounds of a mixture worth 90¢ per pound. First, circle what you are trying to find— how many pounds of each type.Now, let the number of pounds of $1.05 coffee be denoted as x.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.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 luck out a bit in this problem since the price is $1.00 per pound; because we are multiplying by 1, the total cost and the amount are both represented as a 8. But are we any closer to finding out how many pounds of walnuts we need for this mixture? The key to the problem lies in the total cost column.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.The total cost of walnuts, then, will be 0.8a, as walnuts cost $0.80 per 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.

.05 per pound is mixed with coffee worth 85¢ per pound to obtain 20 pounds of a mixture worth 90¢ per pound. First, circle what you are trying to find— how many pounds of each type.

Now, let the number of pounds of

Mixtures (and mixture problems) are made whenever different types of items are combined to create a third, “mixed” item.

Coffee worth $1.05 per pound is mixed with coffee worth 85¢ per pound to obtain 20 pounds of a mixture worth 90¢ per pound. First, circle what you are trying to find— how many pounds of each type.

Now, let the number of pounds of $1.05 coffee be denoted as x.

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.

||

Mixtures (and mixture problems) are made whenever different types of items are combined to create a third, “mixed” item.Coffee worth $1.05 per pound is mixed with coffee worth 85¢ per pound to obtain 20 pounds of a mixture worth 90¢ per pound. First, circle what you are trying to find— how many pounds of each type.Now, let the number of pounds of $1.05 coffee be denoted as x.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.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 luck out a bit in this problem since the price is $1.00 per pound; because we are multiplying by 1, the total cost and the amount are both represented as a 8. But are we any closer to finding out how many pounds of walnuts we need for this mixture? The key to the problem lies in the total cost column.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.The total cost of walnuts, then, will be 0.8a, as walnuts cost $0.80 per 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.

.05 coffee be denoted as x.

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.

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