Movie theater a has a popcorn machine with 120 gallon capacity. It sells 7 gallons of popcorn per hour movie theater B has a popcorn machine with 150 gallon capacity. It sells 9 gallons of popcorn per hour right and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.
Let's represent the amount of popcorn left in theater A after x hours as P(x) and the amount of popcorn left in theater B after x hours as Q(x).
From the given information, we know that:
P(0) = 120 (initial capacity of theater A)
Q(0) = 150 (initial capacity of theater B)
P(x) = 120 - 7x (popcorn left in theater A after x hours)
Q(x) = 150 - 9x (popcorn left in theater B after x hours)
To find when the two theaters will have the same amount of popcorn left, we need to solve the equation P(x) = Q(x).
120 - 7x = 150 - 9x
To simplify, we combine like terms:
9x - 7x = 150 - 120
2x = 30
Dividing both sides by 2:
x = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.
Let's start by assuming t to be the number of hours passed since the popcorn machines started selling popcorn.
For Movie theater A, the amount of popcorn left after t hours can be represented by the equation:
120 - 7t
Similarly, for Movie theater B, the amount of popcorn left after t hours can be represented by the equation:
150 - 9t
To find when the two popcorn machines will have the same amount of popcorn left, we can set the two equations equal to each other and solve for t:
120 - 7t = 150 - 9t
First, let's simplify the equation:
-7t + 9t = 150 - 120
2t = 30
Now, let's isolate t:
t = 30/2
t = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.
To solve for the time when the two popcorn machines will have the same amount of popcorn left, we can set up an equation based on the information given.
Let's assume "t" represents the number of hours after which the two popcorn machines will have the same amount of popcorn left.
For theater A, the amount of popcorn remaining after "t" hours can be calculated by: 120 - 7t (since it sells 7 gallons per hour).
Similarly, for theater B, the amount of popcorn remaining after "t" hours can be calculated by: 150 - 9t (since it sells 9 gallons per hour).
To find when the two theaters will have the same amount of popcorn left, we need to set up an equation:
120 - 7t = 150 - 9t
Now, let's solve for "t":
120 - 7t + 7t = 150 - 7t + 9t
120 = 150 + 2t
Subtracting 150 from both sides:
120 - 150 = 150 + 2t - 150
-30 = 2t
Finally, dividing both sides by 2:
-30/2 = 2t/2 → -15 = t
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.