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)
Responses

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

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

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

100−3x=150−5x

1 answer

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

Let's denote \( x \) as the number of hours that have passed.

For Movie Theatre A:

Starting capacity: 100 gallons
Sales rate: 3 gallons per hour
Amount of popcorn left after \( x \) hours: \( 100 - 3x \)

For Movie Theatre B:

Starting capacity: 150 gallons
Sales rate: 5 gallons per hour
Amount of popcorn left after \( x \) hours: \( 150 - 5x \)

We want to find when the amount of popcorn left in both machines is equal, so we set the two expressions equal to each other:

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

This equation can be rewritten as:

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

So the correct response is:

3x - 100 = 5x - 150