A science teacher has a supply of 50% sugar solution and a supply of 80% sugar solution. How much of each solution should the teacher mix together to get 105 ML of 60% sugar solution for an experiment

a. 70 ML of the 50% solution and 35 ML of the 80% solution***
b. 35 ML of the 50% solution and 70 ML of the 80% solution
c. 70 ML of the 50% solution and 70 ML of the 80% solution
d. 35 ML of the 50% solution and 35 ML of the 80% solution

You could have just said they were right, there was no reason to be snarky about it.

correct, too easy.

To solve this problem, we need to use the concept of mixtures.

Let's assume that the teacher mixes x milliliters of the 50% sugar solution and y milliliters of the 80% sugar solution.

Since the total volume of the mixture is 105 mL, we have the equation:
x + y = 105 -- Equation 1

To find the percentage of sugar in the mixture, we need to consider the amount of sugar from each solution. The amount of sugar from the 50% solution is 0.5x (since it's 50% sugar) and the amount of sugar from the 80% solution is 0.8y (since it's 80% sugar).

The total amount of sugar in the mixture is (0.5x + 0.8y) mL.

Since we want a 60% sugar solution, we set up the equation:
(0.5x + 0.8y) / 105 = 0.6 -- Equation 2

To solve this system of equations, we can use the substitution method. Rearrange Equation 1 to get x = 105 - y, and substitute this into Equation 2:

(0.5(105 - y) + 0.8y) / 105 = 0.6

Simplifying this equation, we get:
52.5 - 0.5y + 0.8y = 63
0.3y = 63 - 52.5
0.3y = 10.5
y = 10.5 / 0.3
y ≈ 35

Now, substitute this value of y back into Equation 1 to solve for x:
x + 35 = 105
x = 105 - 35
x = 70

Therefore, the teacher should mix 70 mL of the 50% sugar solution and 35 mL of the 80% sugar solution to get 105 mL of a 60% sugar solution.

So, the correct answer is a. 70 mL of the 50% solution and 35 mL of the 80% solution.