Let's solve this step by step:

We are given:

1. A total of 120 children go on the activity holiday.
2. The ratio of girls to boys is $3:5$.
3. 16/25 of the boys go climbing.
4. Twice as many girls go sailing as go climbing.
5. We need to calculate how many children go sailing on Sunday.

Step 1: Calculate the number of girls and boys.

The ratio of girls to boys is $3:5$. So, if there are $3x$ girls, there will be $5x$ boys. The total number of children is 120: $3x + 5x = 120$ $8x = 120 \quad \Rightarrow \quad x = \frac{120}{8} = 15$ So, there are:

• $3x = 3 \times 15 = 45$ girls
• $5x = 5 \times 15 = 75$ boys

Step 2: Calculate the number of boys who go climbing and sailing.

We are told that $\frac{16}{25}$ of the boys go climbing. So, the number of boys who go climbing is: $\frac{16}{25} \times 75 = \frac{16 \times 75}{25} = 48$ The remaining boys go sailing. Therefore, the number of boys who go sailing is: $75 - 48 = 27$

Step 3: Calculate the number of girls who go climbing and sailing.

We know that twice as many girls go sailing as go climbing. Let the number of girls who go climbing be $g_c$. Then the number of girls who go sailing is $2g_c$. The total number of girls is 45, so: $g_c + 2g_c = 45$ $3g_c = 45 \quad \Rightarrow \quad g_c = \frac{45}{3} = 15$ Thus, 15 girls go climbing, and $2 \times 15 = 30$ girls go sailing.

Step 4: Calculate the total number of children going sailing.

The total number of children who go sailing is the sum of the boys and girls who go sailing: $27 \text{ boys} + 30 \text{ girls} = 57 \text{ children}$

Therefore, 57 children go sailing on Sunday.

Would you like more details on any of the steps? Here are 5 questions to extend your understanding:

1. How would the problem change if a different ratio of boys to girls was given?
2. Can you explain why multiplying by $\frac{16}{25}$ gives the number of boys climbing?
3. How would you solve for the number of girls climbing if the ratio between sailing and climbing girls was different?
4. What happens to the total number of children sailing if more boys went climbing?
5. How does the number of children affect the outcome if the total number was more than 120?

Tip: When dealing with ratios, always simplify them to work with the smallest integers possible, as this makes calculations much easier.