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

Answer 1

To find when the two popcorn machines will have the same amount of popcorn left, we can start by setting up the equations based on their initial capacities and rates of sale.

For Movie Theatre A:

• Initial capacity: 100 gallons
• Rate of sale: 3 gallons per hour

The amount of popcorn left in Theatre A at time \(x\) (in hours) can be expressed as: \[ 100 - 3x \]

For Movie Theatre B:

• Initial capacity: 150 gallons
• Rate of sale: 5 gallons per hour

The amount of popcorn left in Theatre B at time \(x\) can be expressed as: \[ 150 - 5x \]

To find when the popcorn amounts are the same, we set these two expressions equal to each other: \[ 100 - 3x = 150 - 5x \]

This gives us the equation that shows when both machines have the same amount of popcorn left. So, the correct response is: \[ 100 - 3x = 150 - 5x \]