Let's solve this step by step:

1. Initial amount of juice in the bottle: The bottle is 24 liters and is three-quarters full. $\text{Amount of juice initially} = \frac{3}{4} \times 24 = 18 \text{ liters}$

2. Juice consumed: You drink a quarter of the juice that was in the bottle. $\text{Juice consumed} = \frac{1}{4} \times 18 = 4.5 \text{ liters}$

3. Juice left in the bottle: Subtract the amount of juice consumed from the initial amount. $\text{Juice left} = 18 - 4.5 = 13.5 \text{ liters}$

So, 13.5 liters of juice is left in the bottle.

Would you like more details or have any questions about the process?

Here are 5 related questions:

1. How much juice would be left if you drank half of the remaining juice instead of a quarter?
2. What fraction of the total bottle is now full?
3. If the bottle was only half full initially, how much juice would be left after drinking a quarter of it?
4. How much juice would be left if the bottle was originally full and you drank a quarter of it?
5. How many liters would you need to drink to leave exactly 10 liters in the bottle?

Tip: When working with fractions of quantities, always find the initial amount first before applying further fractions or percentages.