Snape has 2000 mL of a magic potion solution that is $30/%$ DeMuggle Juice. He also has hundreds of 25 mL bottles that are full of $75/%$ DeMuggle Juice solution. Every time he waves his wand, one of these bottles is added to his magic potion. How many times must he wave his wand to have a solution that is at least $34/%$ DeMuggle Juice?

Snape must wave his wand 8 times.

Explanation:

To determinate the concentration of a final solution that was prepared to mix different solutions of the same solute, we can use the equation:

C1V1 + C2V2 + ... + CnVn = CFVF

Where C is the concentration, V is the volume, 1, 2 ..., n refer for the different solutions, and F refers tho the final solution.

C1 = 0.3 and V1 = 2000 mL

There will be n solution with C = 0.75 and V = 25 mL, then:

0.3x2000 + n (0.75 x 25) = 0.34VF

VF is the final volume, which must be the sum of all the solutions:

VF = 2000 + 25n. Then:

600 + 18.75n = 0.34 (2000 + 25n)

600 + 18.75n = 680 + 8.50n

18.75n - 8.50n = 680 - 600

10.25n = 80

n = 80/10.25

n = 7.80

So, Snape must wave his wand 8 times (7 times will not achieve 34%).