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 galllons of popcorn per hour. write an equation to show when the two popcorn machines will have the same anount of popcorn left

Answer 1

To create an equation for when the popcorn machines at Movie Theatre A and Movie Theatre B have the same amount of popcorn left, we can define the variables involved:

Let:

• \( t \) = time in hours

For Movie Theatre A:

• Initial amount of popcorn = 100 gallons
• Rate of popcorn sold = 3 gallons per hour

The amount of popcorn left in Theatre A after \( t \) hours is given by: \[ \text{Popcorn left in A} = 100 - 3t \]

For Movie Theatre B:

• Initial amount of popcorn = 150 gallons
• Rate of popcorn sold = 5 gallons per hour

The amount of popcorn left in Theatre B after \( t \) hours is given by: \[ \text{Popcorn left in B} = 150 - 5t \]

Setting the two equations equal:

We want to find the time \( t \) when the amounts of popcorn left in both theatres are the same: \[ 100 - 3t = 150 - 5t \]

Solving the equation:

1. Rearranging to isolate \( t \): \[ 5t - 3t = 150 - 100 \] \[ 2t = 50 \] \[ t = 25 \]

Conclusion:

The two popcorn machines will have the same amount of popcorn left after 25 hours.

So the equation representing when the two machines have the same amount of popcorn left is: \[ 100 - 3t = 150 - 5t \]