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

8

Explanation:

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

`volume percent = (volume of solute)/(volume of solution) * 100` (1)

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

`34 = (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 = (600 + 18.75*n )/(2000 + 25*n) *100`

`(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)

`(600+(18.75*8))/(2000+(25*8)) *100 = 34.0909`