Question

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)
12x + 180 = 15x + 210
12x + 210 = 15x + 180
210 − 12x = 180 − 15x
12x − 210 = 15x − 180

Answer 1

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:

```plaintext
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.