Question

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)
• 120 - 7х = 150 - 9x ; x = 15
120 + 7x = 150 + 9x
; x = -15
• 120х - 7 = 150х - 9; x = 15
• 120 — 7х = 150 - 9 ; x = 10

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 their capacities and the rate at which they sell popcorn.

Let \( x \) be the number of hours after opening.

**For Movie Theatre A:**
- Initial Capacity: 120 gallons
- Rate of Sale: 7 gallons/hour
- Amount of popcorn left after \( x \) hours: \( 120 - 7x \)

**For Movie Theatre B:**
- Initial Capacity: 150 gallons
- Rate of Sale: 9 gallons/hour
- Amount of popcorn left after \( x \) hours: \( 150 - 9x \)

We want to find out when the amounts are equal:

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

Now we can solve the equation.

1. Rearranging 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:

\( x = 15 \)

So, the correct equation is:

**\( 120 - 7x = 150 - 9x \); \( x = 15 \)**

Thus, at \( x = 15 \) hours, both popcorn machines will have the same amount of popcorn left.