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=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

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=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

Answer 1

The correct equation is: 120 - 7x = 150 - 9x.

Solving for x:

120 - 7x = 150 - 9x
Adding 9x to both sides:
120 + 2x = 150
Subtracting 120 from both sides:
2x = 30
Dividing both sides by 2:
x = 15

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