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=−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
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

Answer 1

To determine when both popcorn machines will have the same amount of popcorn left, we need to set up an equation. We start by noting the initial capacities and the rates at which they sell popcorn.

1. Let \( x \) be the number of hours elapsed.
2. The amount of popcorn left in Movie Theatre A after \( x \) hours is given by: \[ 120 - 7x \]
3. The amount of popcorn left in Movie Theatre B after \( x \) hours is given by: \[ 150 - 9x \]

We want to find when these two amounts are equal: \[ 120 - 7x = 150 - 9x \]

To solve for \( x \), we first rearrange the equation:

1. Add \( 9x \) to both sides: \[ 120 - 7x + 9x = 150 \] This simplifies to: \[ 120 + 2x = 150 \]

2. Subtract 120 from both sides: \[ 2x = 30 \]

3. 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 response is: \[ 120 - 7x = 150 - 9x; , x = 15 \]