Movie theater A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie theater 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.
Let's assume t hours have passed since the popcorn machines were filled with popcorn.
The amount of popcorn remaining in Theater A after t hours is given by 120 - 7t.
The amount of popcorn remaining in Theater B after t hours is given by 150 - 9t.
To find when the two popcorn machines will have the same amount of popcorn left, we can set the two expressions equal to each other and solve for t:
120 - 7t = 150 - 9t
Simplifying the equation, we get:
2t = 30
Dividing both sides by 2, we find that:
t = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.