Samir and Ben are planning a day trip with their friends. Samir wants to go to a waterpark that charges $40 per person for admission, plus $5 per person for tube rentals. Ben wants to go to a rock-climbing gym that charges $150 to rent the facility, plus an additional $20 per person.
Which equation can you use to find p, the number of people who would need to go on the trip for the two options to cost the same?

We are tasked with finding when the cost of Samir's waterpark trip equals the cost of Ben's rock-climbing gym trip.

### 1. Cost of Samir's waterpark:
- Admission per person: $40
- Tube rentals per person: $5
- Total cost per person: $ 40 + 5 = 45 $
- Total cost for $ p $ people: $ 45p $

### 2. Cost of Ben's rock-climbing gym:
- Facility rental: $150
- Cost per person: $20
- Total cost for $ p $ people: $ 150 + 20p $

### Equation:
To find when the costs are the same, set the total cost of the waterpark equal to the total cost of the rock-climbing gym:

\[
45p = 150 + 20p
\]

This equation can be used to find $ p $, the number of people for which the two options will cost the same.

Do you want further details on how to solve the equation, or do you have any other questions?

### Related Questions:
1. What is the solution for $ p $ in the equation $ 45p = 150 + 20p $?
2. How does the total cost change if the number of people increases by 5 for both plans?
3. What is the total cost for 10 people at the waterpark? At the rock-climbing gym?
4. How would a discount at the waterpark affect the breakeven point?
5. What is the smallest group size for which Ben’s gym becomes more economical?

### Tip:
When comparing costs, identify fixed costs (like the facility rental) and variable costs (like per-person charges) separately to better understand the price structure.

Samir and Ben are planning a day trip with their friends. Samir wants to go to a waterpark that charges $40 per person for admission, plus $5 per person for tube rentals. Ben wants to go to a rock-climbing gym that charges $150 to rent the facility, plus an additional $20 per person. Which equation can you use to find p, the number of people who would need to go on the trip for the two options to cost the same?

Explore how to use linear equations to compare the cost of Samir's waterpark and Ben's rock-climbing gym. This math problem involves finding the number of people (p) for which the costs of both activities will be equal. Suitable for students in Grades 6-8.

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