Movie Theatre A has a popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcorn per hour. Movie

Question

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)
• 3х - 100 = 5х - 150
• 100 - 3х = 150 - 5х
• 100 + 3х = 150 + 5х
О 150 + 3x = 100 + 5х

Answer 1

To determine when the two popcorn machines will have the same amount of popcorn left, we can set up an equation based on the capacity of each machine and the rate at which they sell popcorn.

Let's denote:

• \( x \) as the number of hours.

• For Theatre A (100-gallon capacity, 3 gallons/hour):

  • Amount of popcorn left = \( 100 - 3x \)

• For Theatre B (150-gallon capacity, 5 gallons/hour):

  • Amount of popcorn left = \( 150 - 5x \)

We want to find when the amount of popcorn left in both theatres is equal:

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

This matches the option:

• 100 - 3x = 150 - 5x

Thus, the correct equation is \( 100 - 3x = 150 - 5x \).