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 minus 7 x equals 150 minus 9 x ; x equals 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
None of the given equations are correct. The correct equation is 120 - 7x =150 - 9x. To solve for x, you would subtract 120 from both sides and add 9x to both sides to get 2x = 30. Dividing both sides by 2 gives 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, where x represents the number of hours.
To solve the equation:
120 - 7x = 150 - 9x
Combine like terms:
120 + 2x = 150
Subtract 120 from both sides:
2x = 30
Divide both sides by 2:
x = 15
Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.