To compare the amount of popcorn left in each machine over time, we can set up equations for the amount of popcorn remaining in each machine after \( x \) hours.
For Movie Theatre A:
- Capacity: 100 gallons
- Sells: 3 gallons per hour
- Amount of popcorn left after \( x \) hours: \[ 100 - 3x \]
For Movie Theatre B:
- Capacity: 150 gallons
- Sells: 5 gallons per hour
- Amount of popcorn left after \( x \) hours: \[ 150 - 5x \]
To find when the two machines have the same amount of popcorn left, we can set the two equations equal to each other:
\[ 100 - 3x = 150 - 5x \]
This is the equation that shows when the two popcorn machines will have the same amount of popcorn left.