The entry fee to an amusement park is $ P and children enter at half-price.

Find a formula for a family of 7 (4 adults and 3 children) in terms of P.


To determine the total cost for a family of 7 (4 adults and 3 children) to enter the amusement park, given that the price for children is half the price of adults, we can derive the formula as follows:

- Let the price for an adult ticket be $ P $.
- Since children enter at half-price, the price for a child ticket is $ \frac{P}{2} $.

For the family:
- The total cost for 4 adults = $ 4P $
- The total cost for 3 children = $ 3 \times \frac{P}{2} = \frac{3P}{2} $

Thus, the total cost for the family of 7 is:

\[
\text{Total cost} = 4P + \frac{3P}{2}
\]

To simplify, express both terms with a common denominator:

\[
\text{Total cost} = \frac{8P}{2} + \frac{3P}{2} = \frac{11P}{2}
\]

### Final Formula:
\[
\text{Total cost} = \frac{11P}{2}
\]

This is the formula for the total cost of entry for the family of 7 in terms of $ P $.

Would you like further explanation or have any questions? Here are some related questions to explore:

1. What would the total cost be if $ P $ is $30?
2. How would the formula change if there were 5 children instead of 3?
3. How does the formula change if children get a 25% discount instead of half-price?
4. What is the per-person cost in the family of 7 based on the formula?
5. What is the percentage of the total cost contributed by the children?

**Tip**: When solving for the total cost of groups with varying prices, always try to express everything in terms of a single variable to simplify the calculation.

The entry fee to an amusement park is $P and children enter at half-price. Find a formula for a family of 7 (4 adults and 3 children) in terms of P.

Discover how to calculate the total entry cost for a family of 7 (4 adults and 3 children) at an amusement park where children enter at half-price. This step-by-step solution simplifies the problem into an easy-to-use formula: (11P)/2. Perfect for students in Grades 6-8 learning algebra and basic cost calculations.

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