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.**

**
**