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 an equation to show when the two popcorn machines will have the same amount of popcorn left
Let's assume that after "x" hours, both popcorn machines will have the same amount of popcorn left.
For Movie Theatre A, the amount of popcorn left after "x" hours can be calculated as:
120 - 7x
For Movie Theatre B, the amount of popcorn left after "x" hours can be calculated as:
150 - 9x
To find when the two popcorn machines will have the same amount of popcorn left, we can set these two equations equal to each other:
120 - 7x = 150 - 9x
Simplifying this equation, we get:
2x = 30
x = 15
Therefore, after 15 hours, both popcorn machines will have the same amount of popcorn left.
Let P be the amount of popcorn left in gallons, T be the time in hours since the popcorn machines started operating.
For Movie Theatre A:
P(A) = 120 - 7T
For Movie Theatre B:
P(B) = 150 - 9T
To find when the two popcorn machines will have the same amount of popcorn left, we set P(A) equal to P(B) and solve for T:
120 - 7T = 150 - 9T