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 minus 3 x equals 150 minus 5 x

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

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 have the same amount of popcorn left, we set up the equations based on their capacities and sales rates.

For Movie Theatre A:

• Starting capacity = 100 gallons
• Sales rate = 3 gallons per hour
• Amount left after x hours = \( 100 - 3x \)

For Movie Theatre B:

• Starting capacity = 150 gallons
• Sales rate = 5 gallons per hour
• Amount left after x hours = \( 150 - 5x \)

We want to find the time \( x \) when both machines have the same amount of popcorn left, which gives us the equation:

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

Thus, the correct equation is:

100 - 3x = 150 - 5x