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Movie Theatre A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity. It sells 9 gallons of popcorn per hour. Write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.(1 point) Responses 120−7x=150−9x ; x=10 120 minus 7 x equals 150 minus 9 x ; x equals 10 120x−7=150x−9 ; x=15 120 x minus 7 equals 150 x minus 9 ; x equals 15 120−7x=150−9x ; x=15 120 minus 7 x equals 150 minus 9 x ; x equals 15 120+7x=150+9x ; x=−15

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To find when the two popcorn machines will have the same amount of popcorn left, we can set up an equation based on their initial capacities and rates of sale.

Let \( x \) be the number of hours that have passed.

For Movie Theatre A:

  • Initial capacity = 120 gallons
  • Sales rate = 7 gallons/hour
  • Amount left after \( x \) hours = \( 120 - 7x \)

For Movie Theatre B:

  • Initial capacity = 150 gallons
  • Sales rate = 9 gallons/hour
  • Amount left after \( x \) hours = \( 150 - 9x \)

Set the two expressions equal to each other to find \( x \): \[ 120 - 7x = 150 - 9x \]

Now, solve for \( x \):

  1. Add \( 9x \) to both sides: \[ 120 + 2x = 150 \]

  2. Subtract 120 from both sides: \[ 2x = 30 \]

  3. Divide by 2: \[ x = 15 \]

Thus, the two popcorn machines will have the same amount of popcorn left after 15 hours. The correct response is: 120 - 7x = 150 - 9x; x = 15.