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

Question

as your variable.(1 point)
Responses

150+3x=100+5x
150 plus 3 x equals 100 plus 5 x

100−3x=150−5x
100 minus 3 x equals 150 minus 5 x

3x−100=5x−150
3 x minus 100 equals 5 x minus 150

100+3x=150+5x

Answer 1

To determine when the two popcorn machines will have the same amount of popcorn left, we can set up an equation using their capacities and the rate at which they sell popcorn.

Let \( x \) represent the number of hours after they start selling popcorn.

• For Movie Theatre A:

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

• For Movie Theatre B:

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

To find when the amounts are equal, we can set the equations equal to each other:

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

Thus, the correct equation that shows when the two popcorn machines will have the same amount of popcorn left is:

100 - 3x = 150 - 5x