Question

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

Answer 1

Answer:

8

Step-by-step explanation:

We use the equation for the percentage of solute concentration in a solution:

$volume percent = \frac{volume of solute}{volume of solution} * 100$   (1)

In this case the equiation (1) is transformed into:

$34 = \frac{Total volume of DeMuggle juice}{Total volume of the magic potion} * 100$   (2)

n = number of times he must waves his wand to have a solution that is at least 34% DeMuggle juice.

Vpo = Initial volume of the magic potion = 2000ml

Vjo= Initial volume of DeMuggle juice = 30% * Vpo = (0.3)2000 = 600ml

Vb= Volume of a bottle = 25ml

Vjb = DeMuggle juice volume in a bottle = 75% * Vb = (0.75)25= 18.75ml

Vpmt = Total volume of the magic potion = 2000 + 25*n = Vpo + Vb * n

Vjt = Total volume of DeMuggle juice = 600 + 18.75*n = Vjo + Vjb * n

Replacing in (2):

$34 = \frac{600 + 18.75*n }{2000 + 25*n} *100$

$\frac{34}{100} (2000 + 25*n) = (600 + 18.75* n)$

$680+8.5*n=600+18.75*n$

$80 = 10.25*n$

$n = 7.8$

Since the number of times the wand should be waved must be an integer, it approximates 8

Replacing n=8 in (1)

$\frac{600+(18.75*8)}{2000+(25*8)} *100 = 34.0909$