Question

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.