Question

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

Answer 1

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.