Snape has 2000 mL of a magic potion 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?

Question

Please walk me through this problem at a 7th grade level, because I do not know how to start or complete this problem. Thank you!

Answer 1

Let A=Total amount of the stronger (75%) DeMuggle juice potion added in ml.
The percent of DeMuggle juice is:
(total DeMuggle juice)/(total volume of potion)
The final total DeMuggle juice is:
2000ml(30%) + A(%75)
=600ml + 0.75A
The final total volume of potion is:
2000ml + A

The final ratio is:
(600ml + 0.75A)/(2000ml + A)

Setting that to the desired strength of %34:
(600ml + 0.75A)/(2000ml + A) = 0.34
600ml + 0.75A = (0.34)(2000ml + A)
600ml + 0.75A = 680ml + 0.34A
0.41A = 80ml
A = ?
How many wand waves to Snape have to do to get to this? (Recall that each wave adds a 25ml bottle.)

Answer 2

32423424.5675

Answer 3

24

Answer 4

-7x+-3

Answer 5

32423424.5675

Answer 6

what does slope mean

Answer 7

Look, the answer is 8.

Answer 8

8 Times

Answer 9

The answer is 8

Answer 10

8 since 80/0.41 is 195.12, so divide by 25 to get 7.8 rounding up gives 8