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) please

1 answer

To compare the amount of popcorn left in each machine over time, we can set up equations for the amount of popcorn remaining in each machine after \( x \) hours.

For Movie Theatre A:

  • Capacity: 100 gallons
  • Sells: 3 gallons per hour
  • Amount of popcorn left after \( x \) hours: \[ 100 - 3x \]

For Movie Theatre B:

  • Capacity: 150 gallons
  • Sells: 5 gallons per hour
  • Amount of popcorn left after \( x \) hours: \[ 150 - 5x \]

To find when the two machines have the same amount of popcorn left, we can set the two equations equal to each other:

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

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