To solve this problem, let's break it down into steps:

Step 1: Define Variables

• Let the total number of people who visited the zoo in January be $N$.
• The number of adults is $\frac{14}{23}N$ (since for every 23 people, 14 were adults).
• The number of children is $\frac{9}{23}N$ (since for every 23 people, 9 were children).

Step 2: Write the Revenue Equation

The total revenue from ticket sales is given by: $15 \times \text{Number of adults} + 8 \times \text{Number of children} = 487296$

Substitute the expressions for the number of adults and children: $15 \times \frac{14}{23}N + 8 \times \frac{9}{23}N = 487296$

Step 3: Simplify the Equation

Combine the terms: $\frac{15 \times 14}{23}N + \frac{8 \times 9}{23}N = 487296$ $\frac{210N + 72N}{23} = 487296$ $\frac{282N}{23} = 487296$

Step 4: Solve for $N$

Multiply both sides by 23: $282N = 487296 \times 23$ $282N = 11207808$

Now, divide by 282 to find $N$: $N = \frac{11207808}{282} = 39744$

Step 5: Calculate the Number of Children

The number of children who visited the zoo is: $\text{Number of children} = \frac{9}{23}N = \frac{9}{23} \times 39744 = 15552$

So, 15,552 children visited the zoo in January.

Would you like further details or have any questions?

Here are 5 related questions to expand on this problem:

1. How many adults visited the zoo in January?
2. What would the total revenue have been if the ticket prices for adults and children were both increased by $2?
3. If the ratio of adults to children was 1:1, how many total visitors would have been necessary to collect the same amount of revenue?
4. If the number of children visiting the zoo increased by 10% in February, how many children visited the zoo in February?
5. How much more revenue would have been collected if 1000 more children visited the zoo in January?

Tip: When solving problems involving ratios, always express the total in terms of the parts of the ratio to simplify calculations.