Movie theater A has a popcorn machine with 100 gallon cap, and sells 3 gallons of popcorn per hour. Movie Theatre 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 x as your variable
The amount of popcorn left in theater A's machine can be represented by the equation y = 100 - 3x, where x is the number of hours that have passed.
The amount of popcorn left in theater B's machine can be represented by the equation y = 150 - 5x, where x is the number of hours that have passed.
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.
Let's assume x represents the number of hours that have passed since the popcorn machines started selling popcorn.
For Movie Theater A, the amount of popcorn left in the machine after x hours can be calculated using the equation:
100 - 3x
For Movie Theater B, the amount of popcorn left in the machine after x hours can be calculated using the equation:
150 - 5x
To find the point at which the two popcorn machines will have the same amount of popcorn left, we can set these two equations equal to each other and solve for x:
100 - 3x = 150 - 5x