 The ticket prices for visitors to a zoo are $15 for adult and $8 for children each. In January, the zoo collected $487 296 in ticket sa;es. For every 23 people that visited the zoo that month, 14 were adults and 9 were children. How many children visited to the zoo in January?

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.

Learn how to calculate the number of children who visited a zoo in January using ratio and proportion concepts. Solve the problem step-by-step with detailed explanations. Suitable for students in Grades 7-9.

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