Table of Contents |
Mixture problems involve combining two or more things, such as chemical solutions. Mixture problems can also involve prices, percents, and other concentrations. These types of problems can be solved by setting up and solving a system of equations. Typically, one equation represents the relationship between the concentration amounts given by the problem, and another equation relates the total quantities involved.
For mixture problems, we usually have to do two things:
Let's consider a classic mixture problem. These problems usually involve mixing chemicals with different percent concentrations, in order to yield a specific amount of a specific percent concentration needed for a lab experiment.
EXAMPLE
You need to prepare 50 mL of a 17% solution of HCl for a lab experiment. You only have two solutions of HCl available to you: a 10% solution, and a 40% solution. How much of each solution should you combine to yield 50 mL of 17% HCl?There are several ways we can solve a system of equations. We can use the addition method, substitution method, or even solve by graphing. If you are dealing with decimal numbers in your system, it probably isn't the easiest to solve by graphing. You may also have trouble solving by the addition method if you don't have terms that would easily cancel through addition. If those fail, you can try solving by substitution.
EXAMPLE
Solve the system of equations to find how many milliliters of 40% and 10% solution we need to mix in order to yield 50 mL of a 17% solution.Using the second equation, isolate x by subtracting both sides by y | |
An equivalent equation to the original |
Using the first equation, substitute in for x | |
Single-variable equation with only y's |
Using this new equation, solve for y by distributing 0.1 into | |
Combine like terms | |
Subtract 5 from both sides | |
Divide both sides by 0.3 | |
Our solution for y (rounded) |
Using the Equivalent equation for , substitute 11.67 in for y | |
Subtract 11.67 from 50 | |
Our solution for x |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License