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

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

120x−7=150x−9
; x=15
120 x minus 7 equals 150 x minus 9 ; x equals 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 an equation based on the information given.

Let \( x \) be the number of hours after the popcorn machines start selling popcorn.

For Movie Theatre A:

• Initial capacity: 120 gallons
• Sells: 7 gallons/hour
• Amount of popcorn left after \( x \) hours: \( 120 - 7x \)

For Movie Theatre B:

• Initial capacity: 150 gallons
• Sells: 9 gallons/hour
• Amount of popcorn left after \( x \) hours: \( 150 - 9x \)

We want to find \( x \) when both machines have the same amount of popcorn left:

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

Now, let's solve the equation step by step.

1. Add \( 9x \) to both sides:

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

This simplifies to:

\[ 120 + 2x = 150 \]

2. Subtract \( 120 \) from both sides:

\[ 2x = 150 - 120 \]

This simplifies to:

\[ 2x = 30 \]

3. Divide both sides by 2:

\[ x = 15 \]

So, the solution to the problem is \( x = 15 \), meaning the two popcorn machines will have the same amount of popcorn left after 15 hours.

The correct option from your list is:

120−7x=150−9x; x=15