Question

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

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

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

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

100+3x=150+5x

Answer 1

To find the equation that shows when both popcorn machines will have the same amount of popcorn left, we need to express the amount of popcorn remaining in each machine as a function of time (hours) represented by \(x\).

For Movie Theatre A:
- Initial capacity: 100 gallons
- Selling rate: 3 gallons per hour

The amount of popcorn left after \(x\) hours will be:
\[ 100 - 3x \]

For Movie Theatre B:
- Initial capacity: 150 gallons
- Selling rate: 5 gallons per hour

The amount of popcorn left after \(x\) hours will be:
\[ 150 - 5x \]

To find when they have the same amount of popcorn left, we set the two equations equal to each other:
\[ 100 - 3x = 150 - 5x \]

Therefore, the correct equation is:
\[ 100 - 3x = 150 - 5x \]