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.
120 - 7t = 150 - 9t
2t = 30
t = 15
after 15 hours, they both will have the same amount of stale popcorn
Let's assume that x represents the number of hours passed since both popcorn machines started selling popcorn.
For Movie Theatre A, the amount of popcorn remaining after x hours would be 120 - 7x gallons.
For Movie Theatre B, the amount of popcorn remaining after x hours would be 150 - 9x gallons.
To find when the two popcorn machines will have the same amount of popcorn left, we set up the equation:
120 - 7x = 150 - 9x
Now, let's solve this equation:
120 + 2x = 150
2x = 150 - 120
2x = 30
x = 30 / 2
x = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.
To solve this problem, let's first define some variables:
Let's call the number of hours passed since the popcorn machines started selling popcorn as "t".
Let P_A be the amount of popcorn left in Theater A's machine after t hours.
Let P_B be the amount of popcorn left in Theater B's machine after t hours.
We know that Theater A sells 7 gallons per hour, so the amount of popcorn left in Theater A's machine after t hours can be calculated as:
P_A = 120 - 7t (since the machine's initial capacity is 120 gallons)
Similarly, Theater B sells 9 gallons per hour, so the amount of popcorn left in Theater B's machine after t hours can be calculated as:
P_B = 150 - 9t (since the machine's initial capacity is 150 gallons)
To find the time when both machines have the same amount of popcorn left, we need to set P_A equal to P_B and solve for t:
120 - 7t = 150 - 9t
Adding 9t to both sides of the equation:
9t - 7t + 120 = 150
Simplifying the equation:
2t = 30
Dividing both sides of the equation by 2:
t = 15
Therefore, after 15 hours, both Movie Theater A and Movie Theater B will have the same amount of popcorn left.