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 In algebra, mixture problems always fall into 1 of 3 categories. A) Mixing 2 solutions to make a third Example: You need 20 liters of 80% antifreeze solution. You have solutions of 75% antifreeze and 95% antifreeze. How much of each do you need to mix together? Using the calculator, we click "A" then enter Volume Needed   20 Concentration Needed   80 Concentration of Solution 1   75 Concentration of Solution 2   95 Clicking "Calculate" we see the answers are: Volume of Solution 1   15 Volume of Solution 2     5

 Without using the calculator: You have 75% and 95% antifreeze solutions and you need 20 liters of 80% antifreeze We set up two equations: x + y = 20 .75x + .95y = (.80 * 20) Then we solve for x and y. B) Changing the Concentration of a solution Example: You have 15 liters of 75% antifreeze. How many liters of 95% antifreeze must be mixed with this to make an 80% antifreeze solution? Using the calculator, we click "B" then enter Solution 1 Volume   15 Solution 1 Concentration   75 Solution 2 Concentration   95 Solution 3 Concentration   80 Clicking "Calculate" we see the answer is: Volume of Solution 2 Needed   5 Without using the calculator: You have 15 liters of 75% antifreeze. How many liters of 95% antifreeze must be mixed with this to make an 80% antifreeze solution? We will only need one equation for this. We have 15 liters of 75% antifreeze to which we will add several liters (or "x") of 95% antifreeze to make an 80% antifreeze solution. .75 * 15 + .95x = .80 * (15 + x) where (15 + x) is the volume of the 80% antifreeze solution. 11.25 + .95x = 12 + .80x .15x = .75 x = 5 liters C) Calculating concentration of final solution Example: 15 liters of 75% antifreeze is mixed with 5 liters of 95% antifreeze. What is the antifreeze percentage of the final solution? Using the calculator, we click "A" then enter Solution 1 Volume   15 Solution 1 Concentration   75 Solution 2 Volume   5 Solution 2 Concentration   95 Clicking "Calculate" we see the answer is: Concentration of Final Solution   80 Without using the calculator: You mix 15 liters of 75% antifreeze with 5 liters of 95% antifreeze. What is the antifreeze percentage of the final solution? Let us calculate the volume of antifreeze in the final solution. 15 * .75 = 11.25 liters of antifreeze. 5 * .95 = 4.75 liters of antifreeze. Equals 16 liters of antifreeze. The total volume of the final solution = 15 + 5 = 20 liters. Therefore, the alcohol percentage = 16 liters / 20 total liters = 80 per cent.
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