To determine when the two popcorn machines will have the same amount of popcorn left, we can represent the amount of popcorn left in each machine as a function of time (in hours).
Let \( x \) be the number of hours after the machines start selling popcorn.
For Movie Theatre A:
- Capacity: 100 gallons
- Selling rate: 3 gallons per hour
- Amount left after \( x \) hours: \( 100 - 3x \)
For Movie Theatre B:
- Capacity: 150 gallons
- Selling rate: 5 gallons per hour
- Amount left after \( x \) hours: \( 150 - 5x \)
To find when both theatres have the same amount of popcorn left, we can set their expressions equal to each other:
\[ 100 - 3x = 150 - 5x \]
This is the correct equation that shows when both popcorn machines will have the same amount of popcorn left.
Now, let’s analyze the options you provided:
- \( 3x - 100 = 5x - 150 \)
- \( 100 + 3x = 150 + 5x \)
- \( 100 - 3x = 150 - 5x \) (This is the correct one)
- \( 150 + 3x = 100 + 5x \)
Thus, the correct choice is: \( 100 - 3x = 150 - 5x \)