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

Question

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

Answer 1

To determine when the two popcorn machines will have the same amount of popcorn left, we need to set up an equation based on the information provided.

Let's denote \( x \) as the number of hours since both machines started operating.

For Theatre A:

• Initial capacity: 100 gallons
• Rate of sale: 3 gallons per hour
• Amount left after \( x \) hours: \( 100 - 3x \)

For Theatre B:

• Initial capacity: 150 gallons
• Rate of sale: 5 gallons per hour
• Amount left after \( x \) hours: \( 150 - 5x \)

We need to set the two amounts equal to each other:

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

This shows that after \( x \) hours, the amount of popcorn left in both machines will be the same.

So the correct equation is:

100 - 3x = 150 - 5x