Answer:
8
Step-by-step explanation:
We use the equation for the percentage of solute concentration in a solution:
[tex]volume percent = \frac{volume of solute}{volume of solution} * 100[/tex] (1)
In this case the equiation (1) is transformed into:
[tex]34 = \frac{Total volume of DeMuggle juice}{Total volume of the magic potion} * 100[/tex] (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):
[tex]34 = \frac{600 + 18.75*n }{2000 + 25*n} *100[/tex]
[tex]\frac{34}{100} (2000 + 25*n) = (600 + 18.75* n)[/tex]
[tex]680+8.5*n=600+18.75*n[/tex]
[tex]80 = 10.25*n[/tex]
[tex]n = 7.8[/tex]
Since the number of times the wand should be waved must be an integer, it approximates 8
Replacing n=8 in (1)
[tex]\frac{600+(18.75*8)}{2000+(25*8)} *100 = 34.0909[/tex]
