Question
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?
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?
Answers
GPT-4o mini
To find the number of people \( p \) for which the costs of the two options are the same, we can set up equations for both options:
1. **Cost for the waterpark**:
- Admission: $40 per person
- Tube rentals: $5 per person
- Total cost for \( p \) people:
\[
C_{waterpark} = 40p + 5p = 45p
\]
2. **Cost for the rock-climbing gym**:
- Facility rental: $150 (fixed cost)
- Additional cost: $20 per person
- Total cost for \( p \) people:
\[
C_{rock_climbing} = 150 + 20p
\]
Now, to find the number of people \( p \) such that the costs are equal, we set the two equations equal to each other:
\[
45p = 150 + 20p
\]
This is the equation you can use to determine the number of people for which the two options cost the same.
1. **Cost for the waterpark**:
- Admission: $40 per person
- Tube rentals: $5 per person
- Total cost for \( p \) people:
\[
C_{waterpark} = 40p + 5p = 45p
\]
2. **Cost for the rock-climbing gym**:
- Facility rental: $150 (fixed cost)
- Additional cost: $20 per person
- Total cost for \( p \) people:
\[
C_{rock_climbing} = 150 + 20p
\]
Now, to find the number of people \( p \) such that the costs are equal, we set the two equations equal to each other:
\[
45p = 150 + 20p
\]
This is the equation you can use to determine the number of people for which the two options cost the same.