movie theater A has popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcorn per hour. movie theater B has a popcorn machine with a 150-gallon capacity, and sells 5 gallons of popcorn per hour. write an equation to show when the 2 popcorn machines will have the same amount of popcorn left. use x as your variable.

Question

a. 150+3x=100+5x
b. 100+3x=150+5x
c. 3x-100=5x-150
d. 100-3x=150-5x

Answer 1

To determine when the two popcorn machines will have the same amount of popcorn left, we need to set up an equation based on the initial capacities and the rates at which they sell popcorn.

1. The initial amount of popcorn in Theater A: 100 gallons
2. The initial amount of popcorn in Theater B: 150 gallons
3. Popcorn sold per hour at Theater A: 3 gallons
4. Popcorn sold per hour at Theater B: 5 gallons

After \(x\) hours, the amount of popcorn left in each theater can be expressed as follows:

• For Theater A: \(100 - 3x\)
• For Theater B: \(150 - 5x\)

We want to find when these two amounts are equal:

\[100 - 3x = 150 - 5x\]

Now, let's rearrange this to see which option matches:

Adding \(5x\) to both sides:

\[100 - 3x + 5x = 150\]

This simplifies to:

\[100 + 2x = 150\]

Now subtracting 100 from both sides:

\[2x = 50\]

So, isolating \(x\):

\[x = 25\]

However, the equation we derived to set equal amounts is \(100 - 3x = 150 - 5x\).

Thus, the correct choice that reflects this equation is:

d. \(100 - 3x = 150 - 5x\).

Answer 2

are you sure

Answer 3

Let's double-check the work to ensure the correct equation for when the two popcorn machines will have the same amount of popcorn left.

Given:

• Theater A:

  • Initial popcorn: 100 gallons
  • Rate of sale: 3 gallons per hour

• Theater B:

  • Initial popcorn: 150 gallons
  • Rate of sale: 5 gallons per hour

Amount of popcorn left after \(x\) hours:

• For Theater A: \[ \text{Popcorn left} = 100 - 3x \]

• For Theater B: \[ \text{Popcorn left} = 150 - 5x \]

Setting the two equations equal to each other:

To find when the amounts are the same, we set: \[ 100 - 3x = 150 - 5x \]

Now, rearranging the equation to isolate \(x\):

1. Add \(5x\) to both sides: \[ 100 - 3x + 5x = 150 \] This simplifies to: \[ 100 + 2x = 150 \]

2. Subtract 100 from both sides: \[ 2x = 50 \]

3. Divide by 2: \[ x = 25 \]

By confirming my previous calculations, the correctly derived equation that represents the situation is indeed: \[ 100 - 3x = 150 - 5x \]

So the answer remains the same:

d. \(100 - 3x = 150 - 5x\) is correct.

Thank you for prompting a review!