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)

Question

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=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

Answer 1

The correct equation is 120 - 7x = 150 - 9x ; x = 15

This equation represents the amount of popcorn remaining at each theater. The left side represents the amount of popcorn remaining in theater A (starting with 120 gallons and decreasing by 7 gallons per hour), and the right side represents the amount of popcorn remaining in theater B (starting with 150 gallons and decreasing by 9 gallons per hour).

Solving the equation, we find that x = 15. This means that after 15 hours, the two theaters will have the same amount of popcorn left.