You are a lab technician and must create 250 ml of a 17% salt-solution.

a. If you have 500 ml of 28% salt-solution, how many milliliters of it should you mix with water in order to create 250 ml of a 17% salt-solution?
b. If you have 400 ml of 40% salt-solution, how many milliliters of it should you mix with water in order to create 250 ml of a 17% salt-solution?
c. If in parts a and b above we use respectively V1 milliliters at salt concentration of C1 and V2 milliliters at salt concentrations of C2 then give a mathematical proof to show that C1/V1=C2/V2.
d. Use the above formula along with the results in part a to determine the number of milligrams of 35% salt-solution would be needed to mix with water to create 250 ml of 17% solution.
e. What is the domain of Ci in the formula in part c?

Hint:

Do this part and the other question will follow.

By the way, this is not calculus.

a. To create a 17% salt-solution, you need to mix a certain amount of the 28% salt-solution with water. Let's denote the volume of the 28% salt-solution as V1 (in ml) that needs to be mixed with water to create 250 ml of the 17% salt-solution.

To find V1, we can use the following formula:

(0.28 * V1) + (0 * (250 - V1)) = 0.17 * 250

In this equation, the left side represents the salt content of the 28% salt-solution mixed with water (since the added water has 0% salt content), and the right side represents the salt content in the final 17% salt-solution.

Simplifying the equation, we get:

0.28 * V1 = 0.17 * 250

Dividing both sides by 0.28, we find:

V1 = (0.17 * 250) / 0.28

Therefore, you should mix approximately 151.8 ml of the 28% salt-solution with water to create 250 ml of a 17% salt-solution.

b. Following the same process as part a, let's denote the volume of the 40% salt-solution as V2 (in ml) that needs to be mixed with water to create 250 ml of the 17% salt-solution.

The equation will be:

(0.40 * V2) + (0 * (250 - V2)) = 0.17 * 250

Simplifying further, we get:

0.40 * V2 = 0.17 * 250

Dividing both sides by 0.40, we find:

V2 = (0.17 * 250) / 0.40

So, you should mix approximately 106.25 ml of the 40% salt-solution with water to create 250 ml of a 17% salt-solution.

c. To prove that C1/V1 = C2/V2, we can substitute the values from parts a and b:

For part a: C1 = 0.28 and V1 = 151.8
For part b: C2 = 0.40 and V2 = 106.25

Substituting these values into C1/V1 = C2/V2:

(0.28 / 151.8) = (0.40 / 106.25)

Cross-multiplying, we get:

(0.28 * 106.25) = (0.40 * 151.8)

Which simplifies to:

29.75 = 60.72

Since the equation is true, we have proven that C1/V1 = C2/V2.

d. To determine the number of milligrams of 35% salt-solution needed in order to create 250 ml of a 17% salt-solution, we can use the formula C1/V1 = C2/V2.

Let's denote the volume of the 35% salt-solution as V3 (in ml) that needs to be mixed with water.

We have the following values:
C1 = 0.35 (salt concentration of the 35% salt-solution)
V1 = ? (unknown volume of the 35% salt-solution)
C2 = 0.17 (target salt concentration of the final solution)
V2 = 250 (volume of the final solution)

Substituting these values into the formula:

0.35/V1 = 0.17/250

Cross-multiplying, we get:

(0.35 * 250) = (0.17 * V1)

Thus, 87.5 = 0.17 * V1

Dividing both sides by 0.17, we find:

V1 = 87.5 / 0.17

Therefore, you would need approximately 514.7 ml of the 35% salt-solution to mix with water to create 250 ml of a 17% salt-solution.

e. The domain of Ci (salt concentration) in the formula from part c is any non-zero positive real number. Since salt concentration cannot be negative and cannot be zero (unless it's pure water), the domain is the set of positive real numbers excluding zero.