Movie Theatre A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity. It sells 9 gallons of popcorn per hour. Write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.
120x−7=150x−9 ; x=15
120−7x=150−9x ; x=10
120−7x=150−9x ; x=15
120+7x=150+9x ; x=−15
The correct equation to show when the two popcorn machines will have the same amount of popcorn left is:
120 - 7x = 150 - 9x
Solving this equation,
120 - 150 = -2x + 9x
-30 = 7x
x = -30/7
So, the two popcorn machines will have the same amount of popcorn left after approximately x = -30/7 hours.