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)%0D%0AResponses%0D%0A%0D%0A120+7x=150+9x ; x=−15%0D%0A120 plus 7 x equals 150 plus 9 x ; x equals negative 15%0D%0A%0D%0A120−7x=150−9x ; x=15%0D%0A120 minus 7 x equals 150 minus 9 x ; x equals 15%0D%0A%0D%0A120x−7=150x−9 ; x=15%0D%0A120 x minus 7 equals 150 x minus 9 ; x equals 15%0D%0A%0D%0A120−7x=150−9x ; x=10%0D%0A120 minus 7 x equals 150 minus 9 x ; x equals 10%0D%0ASkip to navigation%0D%0AHighlight%0D%0A%0D%0Apage 15 of 15

Answer 1

To determine when the two popcorn machines will have the same amount of popcorn left, we need to set up an equation.

Let's let x represent the number of hours that have passed.

For Movie Theatre A, the amount of popcorn remaining (in gallons) after x hours is given by 120 - 7x.

For Movie Theatre B, the amount of popcorn remaining (in gallons) after x hours is given by 150 - 9x.

So, the equation is:

120 - 7x = 150 - 9x

To solve for x, we need to combine like terms:

(-7x + 9x) = (150 - 120)
2x = 30

Divide both sides of the equation by 2:

2x/2 = 30/2
x = 15

Therefore, the two popcorn machines will have the same amount of popcorn left after 15 hours.