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

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

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−210=15x−180

Answer 1

To create an equation that shows when the two machines will have filled the same number of cans of soup, we start by defining the total number of cans each machine will have filled after \( x \) minutes.

For the first machine:

• Initially filled: 180 cans
• Rate: 15 cans per minute
• Cans filled after \( x \) minutes: \( 180 + 15x \)

For the second machine:

• Initially filled: 210 cans
• Rate: 12 cans per minute
• Cans filled after \( x \) minutes: \( 210 + 12x \)

We set these two expressions equal to each other to find out when they will have filled the same number of cans:

\[ 180 + 15x = 210 + 12x \]

Thus, the correct equation is:

15x + 180 = 12x + 210

This matches with the first response option you listed:

12x + 180 = 15x + 210.

Note that this option contains the terms in a different order but represents the same relationship mathematically. However, based on the intended formation, the following corrected version aligns with your response:

15x + 180 = 12x + 210 (after rearranging the terms).

This maintains the same meaning but follows more conventional reading order in terms of \( x \).