Linear Equations in Real-World Scenarios Quick Check

Question

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Question
Movie Theatre A has a popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity, and sells 5 gallons of popcorn per hour. Write an equation to show when the two popcorn machines will have the same amount of popcorn left. Use x
as your variable.(1 point)
Responses

100+3x=150+5x
100 plus 3 x equals 150 plus 5 x

3x−100=5x−150
3 x minus 100 equals 5 x minus 150

100−3x=150−5x
100 minus 3 x equals 150 minus 5 x

150+3x=100+5x

Answer 1

To determine when the two popcorn machines will have the same amount of popcorn left, we can set up equations based on their initial capacities and rates of selling popcorn.

For Movie Theatre A:

• Initial capacity: 100 gallons
• Sells popcorn at a rate of 3 gallons per hour
• Amount of popcorn left after \(x\) hours: \(100 - 3x\)

For Movie Theatre B:

• Initial capacity: 150 gallons
• Sells popcorn at a rate of 5 gallons per hour
• Amount of popcorn left after \(x\) hours: \(150 - 5x\)

To find when the amounts are the same, we set the two equations equal to each other:

\[100 - 3x = 150 - 5x\]

So the correct equation to use is:

100 − 3x = 150 − 5x