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)

Question

Responses

120−7x=150−9x
; x=10
120 minus 7 x equals 150 minus 9 x ; x equals 10

120+7x=150+9x
; x=−15
120 plus 7 x equals 150 plus 9 x ; x equals negative 15

120−7x=150−9x
; x=15
120 minus 7 x equals 150 minus 9 x ; x equals 15

120x−7=150x−9
; x=15

Answer 1

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

Let \( x \) be the number of hours after which the amounts of popcorn will be the same.

For Movie Theatre A:

• Capacity: 120 gallons
• Sales rate: 7 gallons per hour

The amount of popcorn left after \( x \) hours will be: \[ 120 - 7x \]

For Movie Theatre B:

• Capacity: 150 gallons
• Sales rate: 9 gallons per hour

The amount of popcorn left after \( x \) hours will be: \[ 150 - 9x \]

Setting the equations equal:

To find out when both theatres will have the same amount of popcorn left, set the two expressions equal to each other: \[ 120 - 7x = 150 - 9x \]

Solving the equation:

1. Start by simplifying the equation: \[ 120 - 7x = 150 - 9x \]
2. Add \( 9x \) to both sides: \[ 120 + 2x = 150 \]
3. Subtract 120 from both sides: \[ 2x = 30 \]
4. Divide by 2: \[ x = 15 \]

Thus, the correct response is:

\[ 120 - 7x = 150 - 9x \quad ; \quad x = 15 \]

This means that after 15 hours, Movie Theatre A and Movie Theatre B will have the same amount of popcorn left.