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)

Question

Responses

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

100+3x=150+5x

Answer 1

To find when the two popcorn machines will have the same amount of popcorn left, we can express the amount of popcorn left as a function of time (x hours).

For Movie Theatre A:

• Initial amount of popcorn = 100 gallons
• Rate of sale = 3 gallons per hour
• Amount left after x hours = \(100 - 3x\)

For Movie Theatre B:

• Initial amount of popcorn = 150 gallons
• Rate of sale = 5 gallons per hour
• Amount left after x hours = \(150 - 5x\)

We want to find the time \(x\) when the amounts of popcorn left are equal. Thus, we set the two equations equal to each other:

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

So, the correct response is: 100 - 3x = 150 - 5x