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

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

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
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Answer 1

To determine when the amounts of popcorn left in both machines will be equal, we need to set up an equation based on the initial amounts and the rate of selling.

Let \( x \) be the number of hours after the machines start selling popcorn.

- For Theatre A:
- Initial amount of popcorn: 100 gallons
- Rate of selling: 3 gallons per hour
- Amount left after \( x \) hours: \( 100 - 3x \)

- For Theatre B:
- Initial amount of popcorn: 150 gallons
- Rate of selling: 5 gallons per hour
- Amount left after \( x \) hours: \( 150 - 5x \)

We want to set these two expressions equal to find when they will have the same amount of popcorn left:

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

This is the correct equation that shows when the two popcorn machines will have the same amount of popcorn left.

So, the answer is:
\[
100 - 3x = 150 - 5x \quad \text{(Option 3)}
\]