A movie theatre has a popcorn machine with 100 gallons capacity and sells 3 gallons popcorn per hour. The other popcorn machine has 150 capacity and sells 5 gallons per hour. Show equation of the 2 popcorn machines will have the same amount of popcorn left. Use x as variable

Answer 1

Let's assume that after x hours, the popcorn machines will have the same amount of popcorn left.
For the first popcorn machine with a capacity of 100 gallons and selling 3 gallons per hour, the amount of popcorn left after x hours is: 100 - 3x
For the second popcorn machine with a capacity of 150 gallons and selling 5 gallons per hour, the amount of popcorn left after x hours is: 150 - 5x

To find when the two machines will have the same amount of popcorn left, we can set the two equations equal to each other:

100 - 3x = 150 - 5x

To solve for x, we can start by simplifying the equation:

-3x + 5x = 150 - 100
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.