To find an equation representing when the two popcorn machines will have the same amount of popcorn left, we need to establish how much popcorn each machine has after a certain amount of time.
For Movie Theatre A:
- Initial capacity = 100 gallons
- Sales rate = 3 gallons per hour
After \( x \) hours, the popcorn left in Theatre A can be expressed as: \[ 100 - 3x \]
For Movie Theatre B:
- Initial capacity = 150 gallons
- Sales rate = 5 gallons per hour
After \( x \) hours, the popcorn left in Theatre B can be expressed as: \[ 150 - 5x \]
To find when the amount of popcorn left is the same, we set the two expressions equal to each other: \[ 100 - 3x = 150 - 5x \]
Thus, the correct equation is: \[ 100 - 3x = 150 - 5x \]
This falls under the second response:
100−3x=150−5x
100 minus 3 x equals 150 minus 5 x.