Movie theater a has a popcorn machine with 100 gallon capacity and sells 3 gallons of popcorn per hour movie theater B has a popcorn machine with 150 gallon capacity and sells 5 gallons of popcorn per hour. Write an equation to show when the two popcorn machines will have the same amount of popcorn left, use your variable
Let's use the variable x to represent the amount of time in hours.
For movie theater A, the amount of popcorn remaining can be represented by the equation:
A(x) = 100 - 3x
For movie theater B, the amount of popcorn remaining can be represented by the equation:
B(x) = 150 - 5x
To find when the two popcorn machines will have the same amount of popcorn left, we set the two equations equal to each other:
100 - 3x = 150 - 5x
Simplifying the equation:
2x = 50
Dividing both sides by 2:
x = 25
Therefore, the two popcorn machines will have the same amount of popcorn left after 25 hours.
Let's assume that "x" represents the number of hours elapsed.
For movie theater A, the amount of popcorn remaining can be calculated by subtracting the amount of popcorn sold (3 gallons per hour) from the initial capacity (100 gallons). Therefore, for movie theater A, the amount of popcorn remaining can be represented by the equation:
Amount of popcorn remaining in theater A = 100 - 3x
Similarly, for movie theater B, the amount of popcorn remaining can be calculated by subtracting the amount of popcorn sold (5 gallons per hour) from the initial capacity (150 gallons). Therefore, for movie theater B, the amount of popcorn remaining can be represented by the equation:
Amount of popcorn remaining in theater B = 150 - 5x
To find the point when both theaters have the same amount of popcorn remaining, we need to set the two equations equal to each other:
100 - 3x = 150 - 5x
This equation represents the point at which both theaters will have the same amount of popcorn left.
Let's represent the amount of popcorn left in theater A as variable "A" and the amount of popcorn left in theater B as variable "B".
After x hours, theater A will have sold 3x gallons of popcorn, and theater B will have sold 5x gallons of popcorn.
Since theater A starts with a capacity of 100 gallons, the equation representing the amount of popcorn left in theater A after x hours is:
A = 100 - 3x
Similarly, theater B starts with a capacity of 150 gallons, so the equation representing the amount of popcorn left in theater B after x hours is:
B = 150 - 5x
To find out when the two popcorn machines will have the same amount of popcorn left, we need to find the value of x that makes A equal to B:
A = B
Substituting the equations for A and B:
100 - 3x = 150 - 5x
Now we can solve for x to find when the two popcorn machines will have the same amount of popcorn left.