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)

To find the equation that shows when the two machines will have filled the same number of cans, we can set up the equations based on the information provided.

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

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

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

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

So, when we look at the options given in your responses, the correct equation to use when finding when both machines will have filled the same number of cans is: \[ 15x - 180 = 12x - 210 \] Which can be rearranged to the following option: \[ 12x + 210 = 15x + 180 \]

However, based on the format provided in your options, the correct one that matches this would be:

12x + 210 = 15x + 180.

This matches our setup from both machines' respective equations.