Question

movie theatre A has a popcorn machine with a 120 gallon capacity. it sells galllons of popcorn per hour. movie theatre B has a popcorn machine with a 150 gallong capacity. it sellls 9 galllons of popcorn per hour. write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.

120 - 7x = 150 - 9x ; x = 10
120 - 7x = 150 - 9x ; x = 15
120x - 7 =-840 150x - 9 ; x = 15
120 + 7x = 150 + 9x ; x = -15

Answer 1

Let's analyze the problem step by step.

We want to find out when the amount of popcorn left in both machines will be the same. We'll denote \( x \) as the number of hours that pass.

1. **The amount of popcorn left in Theatre A** after \( x \) hours:
\[
\text{Remaining popcorn in A} = 120 - 7x
\]

2. **The amount of popcorn left in Theatre B** after \( x \) hours:
\[
\text{Remaining popcorn in B} = 150 - 9x
\]

Next, we set these two expressions equal to each other to find out when the amounts are the same:
\[
120 - 7x = 150 - 9x
\]

Now, let's solve this equation for \( x \).

3. Start by rearranging the equation:
\[
120 - 7x = 150 - 9x
\]

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

5. Now, subtract \( 120 \) from both sides:
\[
2x = 30
\]

6. Finally, divide by \( 2 \) to solve for \( x \):
\[
x = 15
\]

Thus, the two popcorn machines will have the same amount of popcorn left after **15 hours**.

So the correct equation from the options provided is:

**Correct Option:**
- **120 - 7x = 150 - 9x ; x = 15**