Hmmm...

I'm going to try and solve this in the best way possible (although I might get the answer wrong, so I advise you to read through my explanation first)

Before I start my answer, I want to clarify what you should know:

- how percents work

- how to define a variable

- how to solve a simple algebraic expression

If you don't know any of these, than I advise you to learn as these are major concepts which will help you later on, to make sure that you understand and read my explanation, I will only be giving you the answer to a) so that you can work out (hopefully) the other ones.

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Let's start by clarifying the question, we have:

**red potion** contains 50% of the syrup

**blue potion** contains 15% of the syrup

We want to know how much red potion should be added to 300 ml of blue potion to get a potion which is 20% syrup.

We have 300 ml of blue potion. Let's start by figuring out how much syrup is in the 300 ml.

We have 15% of 300 = 45 ml of syrup

We want 20% of the total to be syrup

We define x as the amount of red potion that goes in to be 20%

Our equation is:

(.50x + 45)/(300 + x) = 20/100

We multiply by 300 + x

(.50x + 45)(100) = (6000+20x)

50x + 4500 = 6000 + 20x

30x = 1500

x = 50

So our equation says that we will add 50ml of red potion, let's confirm:

50 ml of red potion has 25 ml of syrup:

(45 + 25)/(300+50)

70/350 = 20/100 = 1/5

So for **part a) **we need 50ml of red potion, hope you can solve the other ones because I think I gave a pretty solid solution! (If it is wrong please tell me, as I will be happy to fix it!)

~ Hmmmm