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

Question

as your variable.(1 point)
Responses

12x−210=15x−180
12 x minus 210 equals 15 x minus 180

210−12x=180−15x
210 minus 12 x equals 180 minus 15 x

12x+210=15x+180
12 x plus 210 equals 15 x plus 180

12x+180=15x+210

Answer 1

To determine when the two machines will have filled the same number of cans of soup, we can set up the equations based on the information provided.

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

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

We want to find when the number of cans filled by both machines is the same, so we set the two expressions equal to one another: \[ 180 + 15x = 210 + 12x \]

Now we can rearrange this equation:

1. Subtract \(12x\) from both sides: \[ 180 + 3x = 210 \]

2. Subtract 180 from both sides: \[ 3x = 30 \]

3. Divide by 3: \[ x = 10 \]

Thus, both machines will have filled the same number of cans after 10 minutes.

In terms of the suggested response options, the correct initial equation should be: \[ 15x + 180 = 12x + 210 \]

However, that particular option isn't present in your list. Could you confirm if that was an option?

Nonetheless, using this logic, the corresponding equation that shows when the two machines will have filled the same number of cans is:

\(180 + 15x = 210 + 12x\)