Question

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

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

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

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
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Answer 1

To find when the two popcorn machines will have the same amount of popcorn left, we need to consider the initial amount of popcorn each machine has and how much they sell per hour.

Let:

• The amount of popcorn left in Theatre A after \( x \) hours can be expressed as \( 100 - 3x \) (since it starts with 100 gallons and sells 3 gallons per hour).
• The amount of popcorn left in Theatre B after \( x \) hours can be expressed as \( 150 - 5x \) (since it starts with 150 gallons and sells 5 gallons per hour).

We want to set these two expressions equal to each other to find out when the amounts will be the same:

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

So the correct equation representing the scenario is:

100 - 3x = 150 - 5x

This means the first option, which is \( 100 - 3x = 150 - 5x \), is the correct equation.