Linear Equations in Real-World Scenarios Quick Check

Question

5 of 55 of 5 Items
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

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

Answer 1

To find out when the two popcorn machines will have the same amount of popcorn left, we need to set up equations based on the given information.

Let's denote \( x \) as the number of hours after the machines start selling popcorn.

Movie Theatre A:

• Initial capacity: 120 gallons
• Popcorn sold per hour: 7 gallons
• Amount of popcorn left after \( x \) hours: \( 120 - 7x \)

Movie Theatre B:

• Initial capacity: 150 gallons
• Popcorn sold per hour: 9 gallons
• Amount of popcorn left after \( x \) hours: \( 150 - 9x \)

We want to find the value of \( x \) when the amounts of popcorn left are equal:

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

Now, let's solve this equation:

1. Add \( 9x \) to both sides: \[ 120 - 7x + 9x = 150 \] \[ 120 + 2x = 150 \]

2. Subtract \( 120 \) from both sides: \[ 2x = 150 - 120 \] \[ 2x = 30 \]

3. Divide by 2: \[ x = 15 \]

The correct equation is \( 120 - 7x = 150 - 9x \) and the solution is \( x = 15 \).

Therefore, the correct response is: 120−7x=150−9x; x=15.