Question

Movie Theatre A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity. It sells 9 gallons of popcorn per hour. Write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.(1 point) Responses 120−7x=150−9x ; x=15 120 minus 7 x equals 150 minus 9 x ; x equals 15 120x−7=150x−9 ; x=15 120 x minus 7 equals 150 x minus 9 ; x equals 15 120−7x=150−9x ; x=10 120 minus 7 x equals 150 minus 9 x ; x equals 10 120+7x=150+9x ; x=−15

Answer 1

To find out when the two popcorn machines will have the same amount of popcorn left, we can set up the equations based on their capacities and selling rates.

1. The amount of popcorn left in Movie Theatre A after x hours: \[ 120 - 7x \] (since it starts with 120 gallons and sells 7 gallons every hour)

2. The amount of popcorn left in Movie Theatre B after x hours: \[ 150 - 9x \] (since it starts with 150 gallons and sells 9 gallons every hour)

Next, we can set these two equations equal to each other to find out when they have the same amount of popcorn left: \[ 120 - 7x = 150 - 9x \]

Now, let's solve for x.

First, we can add \(9x\) to both sides: \[ 120 - 7x + 9x = 150 \] \[ 120 + 2x = 150 \]

Next, subtract 120 from both sides: \[ 2x = 30 \]

Finally, divide both sides by 2: \[ x = 15 \]

Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.

The correct option indicating this result is:

• \(120 - 7x = 150 - 9x ; x = 15\).