To determine when the two machines will have filled the same number of cans of soup, we need to express the number of cans filled by each machine in terms of the variable \( x \), which represents the time in minutes.
For the first machine:
- It has already filled 180 cans.
- It fills cans at a rate of 15 cans per minute.
- Therefore, the total number of cans filled by the first machine after \( x \) minutes is \( 180 + 15x \).
For the second machine:
- It has already filled 210 cans.
- It fills cans at a rate of 12 cans per minute.
- Thus, the total number of cans filled by the second machine after \( x \) minutes is \( 210 + 12x \).
To find when both machines will have filled the same number of cans, we set these two expressions equal to each other:
\[ 180 + 15x = 210 + 12x. \]
This equation represents the condition when both machines have filled the same number of cans. Therefore, the correct equation from your options is:
180 + 15x = 210 + 12x.
None of the options you provided are correct in the context of this problem, but your equation should be a rewritten form of the one above.
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