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.

Question

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

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 2

are you sure

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!