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

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
120 plus 7 x equals 150 plus 9 x ; x equals negative 15

120−7x=150−9x
; x=15

Answer 1

To determine when the two popcorn machines will have the same amount of popcorn left, we can set up equations representing the amount of popcorn left in each machine after \( x \) hours.

1. The amount of popcorn left in Movie Theatre A after \( x \) hours is: \[ 120 - 7x \] (starting with 120 gallons and selling 7 gallons per hour).

2. The amount of popcorn left in Movie Theatre B after \( x \) hours is: \[ 150 - 9x \] (starting with 150 gallons and selling 9 gallons per hour).

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

Now let's solve the equation:

1. Rearranging terms gives us: \[ 120 - 150 = -9x + 7x \] \[ -30 = -2x \]

2. Dividing both sides by \(-2\) results in: \[ x = 15 \]

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

So the correct response is: 120 - 7x = 150 - 9x; x = 15.