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 gallons of popcorn per hour. Write an equation to show when the two popcorn machines will have the same amount of popcorn left. Use x as your variable.(1 point)

To determine when the amounts of popcorn left in both machines will be equal, we need to set up an equation based on the initial amounts and the rate of selling.

Let \( x \) be the number of hours after the machines start selling popcorn.

• For Theatre A:

  • Initial amount of popcorn: 100 gallons
  • Rate of selling: 3 gallons per hour
  • Amount left after \( x \) hours: \( 100 - 3x \)

• For Theatre B:

  • Initial amount of popcorn: 150 gallons
  • Rate of selling: 5 gallons per hour
  • Amount left after \( x \) hours: \( 150 - 5x \)

We want to set these two expressions equal to find when they will have the same amount of popcorn left:

\[ 100 - 3x = 150 - 5x \]

This is the correct equation that shows when the two popcorn machines will have the same amount of popcorn left.

So, the answer is: \[ 100 - 3x = 150 - 5x \quad \text{(Option 3)} \]