To find when the two popcorn machines will have the same amount of popcorn left, we can set up equations for each theatre based on the starting capacity and the rate at which they sell popcorn.
For Movie Theatre A:
- Initial capacity: 100 gallons
- Sells 3 gallons per hour
- Amount of popcorn left after \( x \) hours: \( 100 - 3x \)
For Movie Theatre B:
- Initial capacity: 150 gallons
- Sells 5 gallons per hour
- Amount of popcorn left after \( x \) hours: \( 150 - 5x \)
To find when both theatres have the same amount of popcorn left, we set the two equations equal to each other:
\[ 100 - 3x = 150 - 5x \]
So, the correct equation is:
\[ 100 - 3x = 150 - 5x \]
This corresponds to the response:
100 plus 3 x equals 150 plus 5 x (100+3x=150+5x)