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

Answer 1

To find out when the two popcorn machines will have the same amount of popcorn left, we need to set up equations based on their capacities and rate of sales.

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

### For Movie Theatre A:
- Initial capacity: 120 gallons
- Sales rate: 7 gallons per hour
- Amount left after \( x \) hours: \( 120 - 7x \)

### For Movie Theatre B:
- Initial capacity: 150 gallons
- Sales rate: 9 gallons per hour
- Amount left after \( x \) hours: \( 150 - 9x \)

### Setting the equations equal:
To find when both machines have the same amount of popcorn left, we set the two expressions equal to each other:

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

### Solving the equation:
1. Rearranging the equation:
\[
120 - 150 = -9x + 7x
\]
\[
-30 = -2x
\]

2. Dividing both sides by -2:
\[
x = 15
\]

### Conclusion:
The two popcorn machines will have the same amount of popcorn left after 15 hours.

Therefore, the correct response is:
120 − 7x = 150 − 9x ; x = 15.