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)

Question

Responses

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

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

Answer 1

To find the equation that shows when the two popcorn machines will have the same amount of popcorn left, we need to express the amount of popcorn left in each machine after \( x \) hours.

For Movie Theatre A:

• Starting capacity: 100 gallons
• Rate of sale: 3 gallons per hour The amount of popcorn left in Theatre A after \( x \) hours is: \[ 100 - 3x \]

For Movie Theatre B:

• Starting capacity: 150 gallons
• Rate of sale: 5 gallons per hour The amount of popcorn left in Theatre B after \( x \) hours is: \[ 150 - 5x \]

To find when the amounts are the same, we set the two equations equal to each other: \[ 100 - 3x = 150 - 5x \]

Rearranging this equation allows us to see that it matches one of the response options, which is: \[ 3x - 100 = 5x - 150 \]

So the correct response is: 3x−100=5x−150