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 plus 3 x equals 150 plus 5 x

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

Answer 1

To find an equation representing when the two popcorn machines will have the same amount of popcorn left, we need to establish how much popcorn each machine has after a certain amount of time.

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

After \( x \) hours, the popcorn left in Theatre A can be expressed as:
\[ 100 - 3x \]

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

After \( x \) hours, the popcorn left in Theatre B can be expressed as:
\[ 150 - 5x \]

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

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

This falls under the second response:
**100−3x=150−5x**
100 minus 3 x equals 150 minus 5 x.