SOLUTION: A container is filled with 56 litres of pine juice. 8 litres of pine juice are extracted and the container is refilled with mango juice. The content of the container is thoroughl

Question 7132: A container is filled with 56 litres of pine juice. 8 litres of pine juice are extracted and the container is refilled with mango juice. The content of the container is thoroughly mixed and 8 litres are then extracted and the container is again refilled with mango juice. What is the ratio of mango juice to pine juice in the final mixture?
Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
We start with 56 litres of pure pine juice. If they take out 8 litres, you'd then have 48 litres left. The mixture is still pure.

If it's refilled with 8 litres of mango juice, the resulting mixture will be 8 parts mango and 48 parts pine, or 1 part mango, 6 parts pine. (AKA, roughly 16.67% mango juice).

Now, if they take out 8 litres from that mixture, that 8 litres will also be 1 part mango and 6 parts pine, leaving you with 48 litres of 1 part mango, 6 parts pine.

Hang on, because it gets tricky from here. We're going to use a formula here:

<---- where there are q[1] litres of p[1] % that we start with, and we add q[2] litres of p[2] % mix, and so we'll end up with a mixture that is (q[1] + q[2]) liters big that will have a different percent mixture p[3] from what we started.

We started with 48 liters that is 16.67% mango. So <---- change the percent to a decimal.

We're going to add 8 liters of pure mango juice, so <--- The 100% mango juice is the 1 in decimal.

As total mix, we'll have litres which is 48 + 8 = 56, BUT the percentage mango of the new mixture will surely be different.

So our equation so far is: . All we have to do is solve for .

<---- simplified

<--- roughly 28.57% mango juice or mango juice. Since mango is 2/7 of the mixture, the other 5/7 is pine. The problem asked for the ratio between mango to pine, and that would be the 2:5.
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