Question

A new theater is being built with 1200 seats. The city requires that more than one parking space be available for every 3 seats in the theater. Which inequality represents the number of parking spaces, p, needed for the new theater?

1) p > 400
2) p < 400
3) p ≥ 400
4) p ≤ 400

Answer 1

The inequality representing the number of parking spaces needed for a theater with 1200 seats, according to the city's requirement, is p > 400.

Step-by-step explanation:

The city requires that more than one parking space be available for every 3 seats in the theater. With 1200 seats in the theater, the requirement can be calculated by dividing the number of seats by 3, which equals 400. Since the number of parking spaces needed must be more than this result, the appropriate inequality representing the number of parking spaces, p, needed for the new theater is: p > 400.

To determine the number of parking spaces needed for the new theater, we need to calculate how many parking spaces are required for each seat in the theater. The city requires more than one parking space for every 3 seats in the theater.To represent this requirement as an inequality, we can divide the total number of seats (1200) by 3 to find the minimum number of parking spaces needed. This gives us 400. Since the city requires more than one parking space for every 3 seats, the correct inequality is p > 400. So, option 1) p > 400 is the correct answer choice.