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 minus 7 x equals 150 minus 9 x ; x equals 15

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

Answer 1

Let's set up the equations for the amount of popcorn left in each theater over time.

1. The amount of popcorn left in Movie Theatre A after \( x \) hours: \[ \text{Popcorn left in Theatre A} = 120 - 7x \]

2. The amount of popcorn left in Movie Theatre B after \( x \) hours: \[ \text{Popcorn left in Theatre B} = 150 - 9x \]

We want to find the time \( x \) when both theatres have the same amount of popcorn left. Thus, we can set the two equations equal to each other:

\[ 120 - 7x = 150 - 9x \]

Now, let's solve for \( x \).

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

2. Subtract 120 from both sides: \[ 2x = 150 - 120 \] \[ 2x = 30 \]

3. Divide both sides by 2: \[ x = 15 \]

Thus, the answer is:

\[ \boxed{x = 15} \]

Now looking at the provided options, the correct equation and solution is:

120 - 7x = 150 - 9x ; x = 15