Movie Theatre A has a popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150 gallon capacity and sells 5 galllons of popcorn per hour. write an equation to resemble this story

Answer 1

To develop an equation that reflects the popcorn sales for both Movie Theatre A and Movie Theatre B, we can introduce variables representing the time in hours and the total popcorn sold.

Let:

• \( t \) = time in hours
• \( A \) = amount of popcorn sold by Theatre A (in gallons)
• \( B \) = amount of popcorn sold by Theatre B (in gallons)

From the information given:

1. Movie Theatre A starts with 100 gallons of popcorn and sells 3 gallons per hour: \[ A = 3t \]

2. Movie Theatre B starts with 150 gallons of popcorn and sells 5 gallons per hour: \[ B = 5t \]

If we want to maintain the constraint that the popcorn sold does not exceed the capacity of the machine, we can also express this as inequalities:

For Theatre A: \[ 3t \leq 100 \]

For Theatre B: \[ 5t \leq 150 \]

These equations and inequalities represent the story of popcorn sales at the two movie theatres.