Question

movie theater A has a popcorn machine with a 120-gallon capacity. it sells 7 gallons of popcorn per hour. movie theater B has a popcorn machine with a 150-gallon capacity. it sells 9 gallons of popcorn per hour. write and solve equation to show when the 2 popcorn machines will have the same amount of popcorn left.
a. 120+7x=150+9x ; x = -15
b. 120-7x=150-9x ; x = 10
c. 120x-7=150x-9 ; x = 15
d. 120-7x=150-9x ; x = 15

Answer 1

are you sure

Answer 2

To find out when the two popcorn machines will have the same amount of popcorn left, we can represent the amount of popcorn left in each machine after \( x \) hours.

For Movie Theater A:
- Initial capacity: 120 gallons
- Popcorn sold per hour: 7 gallons
- Amount left after \( x \) hours: \( 120 - 7x \)

For Movie Theater B:
- Initial capacity: 150 gallons
- Popcorn sold per hour: 9 gallons
- Amount left after \( x \) hours: \( 150 - 9x \)

We want to find \( x \) when the amounts left in both machines are equal:
\[
120 - 7x = 150 - 9x
\]

Now, let's solve for \( x \):

1. Rearrange the equation:
\[
120 - 7x + 9x = 150
\]
\[
120 + 2x = 150
\]

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

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

Therefore, the correct equation that shows when the two popcorn machines will have the same amount of popcorn left is option **d**:
\[
120 - 7x = 150 - 9x \; ; \; x = 15
\]

Answer 3

Let's go through the problem again step by step to ensure we have everything correct.

1. **Define the amount of popcorn left for each theater:**
- Movie Theater A starts with 120 gallons and sells 7 gallons per hour. After \( x \) hours, the amount of popcorn left is:
\[
\text{Amount left in A} = 120 - 7x
\]
- Movie Theater B starts with 150 gallons and sells 9 gallons per hour. After \( x \) hours, the amount of popcorn left is:
\[
\text{Amount left in B} = 150 - 9x
\]

2. **Set the two equations equal to find when they have the same amount left:**
\[
120 - 7x = 150 - 9x
\]

3. **Solve for \( x \):**
- Rearranging the equation:
\[
120 - 7x + 9x = 150
\]
Combine like terms:
\[
120 + 2x = 150
\]

- Subtract 120 from both sides:
\[
2x = 30
\]
- Divide by 2:
\[
x = 15
\]

So we confirm that the solution is indeed correct: \( x = 15 \).

Thus, the correct choice from the provided options is still **d:**
\[
120 - 7x = 150 - 9x; \quad x = 15
\]

Thank you for prompting me to double-check, but the calculations, reasoning, and the answer are correct!