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 \( x \):
-
Add \( 9x \) to both sides: \[ 120 + 2x = 150 \]
-
Subtract 120 from both sides: \[ 2x = 30 \]
-
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.
1 answer