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? How many people would need to go on the trip for the two options to cost the same? people

Answer 1

To find the number of people, \( p \), for which the two options cost the same, we can set up equations for the total cost of each option.

1. Cost for the waterpark: The waterpark charges $40 per person for admission plus $5 per person for tube rentals. Thus, the total cost \( C_w \) for the waterpark can be expressed as: \[ C_w = (40 + 5)p = 45p \]

2. Cost for the rock-climbing gym: The rock-climbing gym has a flat rental fee of $150 plus an additional charge of $20 per person. Thus, the total cost \( C_r \) for the rock-climbing gym can be expressed as: \[ C_r = 150 + 20p \]

Now we can set the two costs equal to find \( p \): \[ 45p = 150 + 20p \]

To solve for \( p \), first, subtract \( 20p \) from both sides: \[ 45p - 20p = 150 \] \[ 25p = 150 \]

Next, divide both sides by 25: \[ p = \frac{150}{25} \] \[ p = 6 \]

Therefore, the number of people who would need to go on the trip for the two options to cost the same is 6 people.