Examples of Setting Up "Mixture" Word Problems

You will be mixing a stronger solution with a weaker solution. The number of liters of the stronger solution is currently unknown; I'll use s to stand for the number of liters of the stronger solution. Then the number of liters of the mixture you're making will be s + 50.

Make a table, with the columns showing the numbers of liters of solutions, the percentage of alcohol in each solution (this is your "rate"), and the number of liters of actual alcohol in each solution.

From the last column, you get the equation:

Solve for the value of the variable. Remember to put appropriate units (in this case, "liters") on your hand-in answer.

I'll use w to stand for the number of ounces of water that are needed. And, since pure water has no salt in it, then the percentage of water that is salt is zero, and the number of ounces of salt is also zero.

From the last column, you get the equation:

Solve for the value of w. Remember to put the appropriate units (in this case, "ounces") on your hand-in answer.

This exercise asks us to make the implicit assumption that the selling price of the mix is based only on the selling price (and amounts) of the inputs. Of course, in real life, the selling price of the mix would be a markup on the cost of the mix, and the cost of the mix would be related to the costs of the inputs, plus the extra costs involved in mixing and re-bagging. But this is algebra, not real life.

The price per pound is the "rate" for this exercise. The sum of the prices of the inputs is assumed to be equal to the total price for the mixture.

From the last row, you see that you have 20 pounds of coffee mixture. This mixture will sell for $139.60. To find the selling price per pound of the mixture, divide ($139.60) by (20 pounds). Simplify the division to find the unit rate.

Remember to put appropriate units (in this case, "dollars per pound") on your hand-in answer.

The cost per pound is the "rate" for this exercise.

You are given the number of pounds of corn, but not the number of pounds of beans. I'll use b to stand for this amount.

The cost of the inputs add to the cost of the mix, which (from the far right column) gives the equation:

Solve for the value of the variable. Remember to put the appropriate units (in this case, "pounds") on your hand-in answer.

The percentage of the punch that comes from actual fruit is the "rate" for this exercise. Since the exercise is asking for a percentage, I will use the variable f.

The sum of the input amounts of juice will equal the total amount of juice in the mixture. You can use the last column to create the equation:

Or you can just eyeball the amounts and notice that 300p must equal 30. Either way, do the division to find the value of the variable. Remember that you're looking for a percentage, so you'll need to convert the decimal solution into percentage form.

Note that, because sugar is 100% sugar, the percentage of sugar in what is added to the bowl, in decimal form, is 1.00.

I will use the variable s to stand for the percentage of sugar in the mixture.

From the bottom row, you see that there are 22 grams of sugar in the 50 grams in the bowl, or ²²/₅₀. Convert the decimal value to percentage form.