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?

Question

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

Answer 1

Let's solve this problem using the method of mixtures.

Let x be the amount of the 50% sugar solution in mL.
Then, 105 - x is the amount of the 80% sugar solution in mL.

The amount of sugar in the 50% solution is 50% of x = 0.5x mL.
The amount of sugar in the 80% solution is 80% of (105 - x) = 0.8(105 - x) mL.

To have a 60% sugar solution, the amount of sugar in the mixture should be 60% of the total solution. So,

0.5x + 0.8(105 - x) = 0.6 * 105.

Now let's solve for x:

0.5x + 0.8(105 - x) = 63
0.5x + 84 - 0.8x = 63
0.5x - 0.8x = 63 - 84
-0.3x = -21
x = -21 / -0.3
x = 70.

Therefore, the teacher should mix 70 mL of the 50% solution and 105 - 70 = 35 mL of the 80% solution.

So, the answer is option A: 70 mL of the 50% solution and 35 mL of the 80% solution.