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

120x−7=150x−9
; x=15
120 x minus 7 equals 150 x minus 9 ; x equals 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

120+7x=150+9x
; x=−15

Answer 1

To find the time \( x \) (in hours) after which both cinema's popcorn machines will have the same amount of popcorn left, we can set up an equation based on the initial capacities and the amounts sold over time.

1. Initial Capacities:

   • Theatre A starts with 120 gallons of popcorn.
   • Theatre B starts with 150 gallons of popcorn.

2. Amounts Sold:

   • Theatre A sells 7 gallons per hour, so after \( x \) hours, it will have: \[ 120 - 7x \text{ gallons left.} \]
   • Theatre B sells 9 gallons per hour, so after \( x \) hours, it will have: \[ 150 - 9x \text{ gallons left.} \]

3. Setting the equations equal to each other: To find when they have the same amount of popcorn left, we set the two expressions equal: \[ 120 - 7x = 150 - 9x. \]

4. Solving the Equation: Now, we can solve for \( x \): \[ 120 - 7x = 150 - 9x. \] Rearranging gives: \[ 9x - 7x = 150 - 120, \] \[ 2x = 30, \] \[ x = 15. \]

Thus, the solution is \( x = 15 \), which means that after 15 hours, both popcorn machines will have the same amount of popcorn left.

The correct response is: 120x−7=150x−9 ; x=15.