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.(1 point)
Responses
120+7x=150+9x
; x=−15
120 plus 7 x equals 150 plus 9 x ; x equals negative 15
120−7x=150−9x
; x=10
120 minus 7 x equals 150 minus 9 x ; x equals 10
120x−7=150x−9
; x=15
120 x minus 7 equals 150 x minus 9 ; x equals 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. The solution to this equation is x = 15. Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.
The correct equation to represent when the two popcorn machines will have the same amount of popcorn left is:
120 - 7x = 150 - 9x
To solve this equation, we can start by combining like terms:
-7x + 9x = 150 - 120
Simplifying further, we have:
2x = 30
Finally, we can solve for x by dividing both sides of the equation by 2:
x = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.