Two machines at a factory are filling cans of soup. One machine has already filled 180 cans of soup, and fills cans at a rate of 15 per minute. The second machine has already filled 210 cans of soup, and fills cans at a rate of 12 per minute. Write an equation to show when the two machines will have filled the same number of cans of soup. Use x as your variable.(1 point)

Question

Responses
1. 12x−210=15x−180
2. 210−12x=180−15x
3. 12x+210=15x+180
4. 12x+180=15x+210
Which answer is it?? choose between 1. 2. 3. and 4.

Answer 1

To find the point at which the two machines will have filled the same number of cans, we can set up the equations based on the number of cans filled over time.

1. The first machine has already filled 180 cans and fills at a rate of 15 cans per minute. So, after \( x \) minutes, the total number of cans filled by the first machine will be: \[ 180 + 15x \]

2. The second machine has already filled 210 cans and fills at a rate of 12 cans per minute. So, after \( x \) minutes, the total number of cans filled by the second machine will be: \[ 210 + 12x \]

To find when the two machines will have filled the same number of cans, we set these two expressions equal to each other: \[ 180 + 15x = 210 + 12x \]

Rearranging this equation gives us: \[ 15x - 12x = 210 - 180 \] \[ 3x = 30 \] \[ x = 10 \]

Now, let's write the equation we derived, which is in the form: \[ 15x - 180 = 12x - 210 \] This can be rearranged to match option 1: \[ 12x - 210 = 15x - 180 \]

Thus, the correct option is 1. 12x−210=15x−180.

Answer 2

Movie Theatre A has a popcorn machine with a 100-gallon capacity, and sells 3 gallons of popcorn per hour. Movie Theatre 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 two popcorn machines will have the same amount of popcorn left. Use x as your variable.(1 point)

Responses
1. 100−3x=150−5x
2. 150+3x=100+5x
3. 3x−100=5x−150
4. 150 100+3x=150+5x
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 3

To find when the two popcorn machines at the movie theatres will have the same amount of popcorn left, we can set up equations based on their capacities and sales rates.

1. Movie Theatre A:

   • Capacity: 100 gallons
   • Sales rate: 3 gallons per hour
   • So after \( x \) hours, the amount of popcorn left in Theatre A will be: \[ 100 - 3x \]

2. Movie Theatre B:

   • Capacity: 150 gallons
   • Sales rate: 5 gallons per hour
   • So after \( x \) hours, the amount of popcorn left in Theatre B will be: \[ 150 - 5x \]

To find when the amounts are equal, we set the two expressions equal to each other: \[ 100 - 3x = 150 - 5x \]

Rearranging gives us: \[ -3x + 5x = 150 - 100 \] \[ 2x = 50 \] \[ x = 25 \]

Now, let's identify the derived equation: \[ 100 - 3x = 150 - 5x \] This can be rewritten to match option 1: \[ 100 - 3x = 150 - 5x \]

Therefore, the correct option is 1. 100−3x=150−5x.

Answer 4

An ice cream shop makes vanilla and chocolate ice cream. The vanilla ice cream machine has a 180-cup capacity, and it sells 20 cups per day. The chocolate ice cream machine has a 140-cup capacity, and it sells 16 cups per day. Write and solve an equation to show when the two machines will have the same amount of ice cream left.(1 point)

Responses
1. 180−20x=140−16x ; x=20
2. 180−20x=140−16x ; x=10
3. 180+16x=140+20x ; x=−10
4. 140+16x=180+20x ; x=10
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 5

To find when the two ice cream machines will have the same amount of ice cream left, we set up equations based on their capacities and sales rates.

1. Vanilla Ice Cream Machine:

   • Capacity: 180 cups
   • Sales rate: 20 cups per day
   • Therefore, after \( x \) days, the amount of vanilla ice cream left will be: \[ 180 - 20x \]

2. Chocolate Ice Cream Machine:

   • Capacity: 140 cups
   • Sales rate: 16 cups per day
   • Therefore, after \( x \) days, the amount of chocolate ice cream left will be: \[ 140 - 16x \]

To find when the amounts of ice cream left are equal, we set the two expressions equal to each other: \[ 180 - 20x = 140 - 16x \]

Now, let's solve the equation:

1. Rearranging gives: \[ 180 - 140 = 20x - 16x \] \[ 40 = 4x \] \[ x = 10 \]

Now, we can summarize the derived equation and the value of \( x \): \[ 180 - 20x = 140 - 16x \quad (This matches option 2) \] And we found \( x = 10 \).

Therefore, the correct option is 2. 180−20x=140−16x ; x=10.

Answer 6

Movie Theatre A has a popcorn machine with a 120-gallon capacity. It sells 7 gallons of popcorn per hour. Movie Theatre B has a popcorn machine with a 150-gallon capacity. It sells 9 gallons of popcorn per hour. Write and solve an equation to show when the two popcorn machines will have the same amount of popcorn left.(1 point)

Responses
1. 120−7x=150−9x ; x=15 12
2. 120−7x=150−9x ; x=10
3. 120+7x=150+9x ; x=−15
4. 120x−7=150x−9 ; x=15
Which answer is it?? Choose between 1. 2. 3. and 4.

Answer 7

To determine when the two popcorn machines will have the same amount of popcorn left, we can set up equations based on their capacities and sales rates.

1. Movie Theatre A:

   • Capacity: 120 gallons
   • Sales rate: 7 gallons per hour
   • Therefore, after \( x \) hours, the amount of popcorn left in Theatre A will be: \[ 120 - 7x \]

2. Movie Theatre B:

   • Capacity: 150 gallons
   • Sales rate: 9 gallons per hour
   • Therefore, after \( x \) hours, the amount of popcorn left in Theatre B will be: \[ 150 - 9x \]

Next, we set the two expressions equal to each other to find when they have the same amount of popcorn left: \[ 120 - 7x = 150 - 9x \]

Now, let's solve the equation:

1. Rearranging gives us: \[ 120 - 150 = -9x + 7x \] \[ -30 = -2x \] \[ 2x = 30 \] \[ x = 15 \]

Now, we can summarize the derived equation and the value of \( x \): \[ 120 - 7x = 150 - 9x \quad (This matches option 1) \] And we found \( x = 15 \).

Therefore, the correct option is 1. 120−7x=150−9x ; x=15.

Answer 8

Thanks Mini Bot! Most of these answer are correct!

Answer 9

You're welcome! I'm glad to hear that the answers were helpful and mostly correct. If you have any more questions or need further assistance, feel free to ask. Enjoy your day! 🍿😊