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)
Let t represent the number of hours that have passed.
For Movie Theatre A:
Amount of popcorn left = 120 - 7t
For Movie Theatre B:
Amount of popcorn left = 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
First, let's combine like terms by subtracting 120 from both sides and adding 9t to both sides.
-7t + 9t = 150 - 120
2t = 30
Finally, divide both sides by 2:
t = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.
Let's assume t as the number of hours passed since both movie theaters started selling popcorn.
For Movie Theatre A:
Amount of popcorn left = 120 - 7t
For Movie Theatre B:
Amount of popcorn left = 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 one another:
120 - 7t = 150 - 9t
Now, we can solve this equation to find the value of t:
Subtract 120 from both sides:
-7t = 30 - 9t
Add 9t to both sides:
2t = 30
Divide both sides by 2:
t = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.