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What type of mixture problem is this?




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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 using this calculator.

  ***** OR using just one unknown
Liters of Y = 20 -X
[.75 X + .95 * (20-X)] / 20 = .80
(.75 X + 19 -.95X) / 20 = .80
(-.20 X / 20) = .80 -19/20
(-.20 X / 20) = -.15
Multiplying both sides by 20
-.20 X = -3.00
X = 15 and (20 -X) = 5


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 antifreeze percentage = 16 liters / 20 total liters = 80 per cent.


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