Linear Equations in Real-World Scenarios Quick Check

Question

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Question
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

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

120x−7=150x−9
; x=15

Answer 1

To find out when the two popcorn machines will have the same amount of popcorn left, we can set up the following equations based on their capacities and the rate at which they sell popcorn.

1. For Theatre A:

   • Initial capacity = 120 gallons
   • Sells = 7 gallons per hour
   • Amount of popcorn left after \(x\) hours = \(120 - 7x\)

2. For Theatre B:

   • Initial capacity = 150 gallons
   • Sells = 9 gallons per hour
   • Amount of popcorn left after \(x\) hours = \(150 - 9x\)

Now, we need to set the two expressions equal to each other:

\[ 120 - 7x = 150 - 9x \]

Now, let's solve for \(x\):

1. Move the \(x\) terms to one side: \[ 9x - 7x = 150 - 120 \] \[ 2x = 30 \]

2. Divide both sides by 2: \[ x = 15 \]

So, the correct response from the options provided is:

120−7x=150−9x ; x=15