We are given that three people, Gaspare, Gustavo, and Guglielmo, together buy 6 kg of sweets for a total of 16 + 24 + 40 = 80 euros. The distribution of the sweets is proportional to the amount each person paid. To find how much Gustavo gets, we will calculate the proportion of the total price that Gustavo paid and use that to find his share of the 6 kg of sweets.

Step-by-Step Solution:

1. Total amount paid: $16 + 24 + 40 = 80 \text{ euros}.$

2. Proportion of the total amount paid by Gustavo: Gustavo paid 24 euros, so his proportion is: $\frac{24}{80} = \frac{3}{10}.$

3. Proportion of the total sweets: Since the distribution of sweets is in proportion to the amount paid, Gustavo will receive $\frac{3}{10}$ of the 6 kg of sweets: $\frac{3}{10} \times 6 = 1.8 \text{ kg}.$

Thus, Gustavo gets 1.8 kg of the sweets.

Would you like a more detailed breakdown, or do you have other questions? Here are some related questions:

1. How much did Gaspare and Guglielmo get in terms of the quantity of sweets?
2. How could we set up a general formula for the distribution of items in proportion to payment?
3. If the total amount spent changed, how would the quantities change for each person?
4. What would happen if they spent an equal amount, but the total quantity of sweets changed?
5. How could this problem be solved using a system of equations?

Tip: When dealing with proportional distribution problems, always begin by calculating each person's share of the total amount, then apply that proportion to the total quantity.