To maintain the same quality of lemonade, we need to preserve the ratio of honey to water used in the original mixture.

Step 1: Calculate the ratio of honey to water in the original lemonade

• Honey: 200 ml
• Water: 3 liters = 3000 ml
• Total people: 15 people

The ratio of honey to water in the original lemonade is: $\frac{\text{Honey}}{\text{Water}} = \frac{200 \, \text{ml}}{3000 \, \text{ml}} = \frac{1}{15}$

This ratio should remain the same in the new lemonade for 3 additional people (i.e., 18 people total).

Step 2: Adjust for the additional people

With 3 additional people, the total number of people becomes: $15 + 3 = 18 \text{ people}$

We can proportionally adjust the water and honey quantities to serve 18 people. Since the original 15-person recipe used 3000 ml of water, we now need to adjust this to 600 ml of water (as specified in the problem).

Step 3: Calculate the amount of honey for 600 ml of water

The original ratio of honey to water is $\frac{1}{15}$. Therefore, to maintain the same ratio in 600 ml of water, the amount of honey should be:

$\text{Honey required} = \frac{1}{15} \times 600 \, \text{ml} = 40 \, \text{ml}$

Conclusion:

To make the same quality of lemonade with 600 ml of water, 40 ml of honey should be added.

Would you like more details or have any questions? Here are some related questions:

1. How can we scale the recipe for more or fewer people?
2. What happens to the taste if we add too much or too little honey?
3. How would the calculation change if the amount of water was given in cups instead of milliliters?
4. How does changing the temperature of the water affect the dissolution of honey?
5. What is the mathematical relationship between the number of people and the ingredients in a recipe?

Tip: Always convert quantities to consistent units (e.g., ml or liters) before calculating ratios.