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)

COURSE TOOLS

120 - 7x = 150 - 9x, x = 10 120x - 7 =150x-9.x=15 120 - 7x =150-9x.x=15 120+7z150+9z.z=-15

Answer 1

To find when the two popcorn machines will have the same amount of popcorn left, we can set up the equations for each theatre based on the information provided.

Let \( x \) be the number of hours after the machines start selling popcorn.

For Movie Theatre A:
- The initial amount of popcorn is 120 gallons.
- It sells 7 gallons per hour.
- The amount of popcorn left after \( x \) hours is given by:
\[
\text{Amount left in A} = 120 - 7x
\]

For Movie Theatre B:
- The initial amount of popcorn is 150 gallons.
- It sells 9 gallons per hour.
- The amount of popcorn left after \( x \) hours is given by:
\[
\text{Amount left in B} = 150 - 9x
\]

To find when the amounts of popcorn left are equal, we set the two equations equal to each other:
\[
120 - 7x = 150 - 9x
\]

Now, we can solve for \( x \). Start by isolating \( x \):

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

2. Subtract 120 from both sides:
\[
2x = 30
\]

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

This means after 15 hours, both popcorn machines will have the same amount of popcorn left.

Let's confirm this:
- Amount left in Movie Theatre A after 15 hours:
\[
120 - 7(15) = 120 - 105 = 15 \text{ gallons}
\]

- Amount left in Movie Theatre B after 15 hours:
\[
150 - 9(15) = 150 - 135 = 15 \text{ gallons}
\]

Both machines will have 15 gallons left after 15 hours.

Thus, the solution is \( x = 15 \) hours.