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

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
12 x minus 210 equals 15 x minus 180

12x+180=15x+210

Answer 1

To set up the equation for the number of cans filled by both machines, we need to express both machines' filled cans in terms of the variable \( x \), where \( x \) represents the number of minutes that have passed.

• The first machine has already filled 180 cans and fills 15 cans per minute, so after \( x \) minutes, it will have filled a total of \( 180 + 15x \) cans.

• The second machine has already filled 210 cans and fills 12 cans per minute, so after \( x \) minutes, it will have filled a total of \( 210 + 12x \) cans.

To find when the two machines will have filled the same number of cans, we can set the two expressions equal to each other:

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

So, the correct response is not listed in your options but should be:

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

This can be rearranged or simplified to find the value of \( x \), but the initial equation represents the situation accurately.

If you need to choose from the provided responses, the most similar format to the correct one is:

210 - 12x = 180 - 15x

This is equivalent upon rearranging but is not written in its simplest form. Thus, it's not ideal but is the closest match to what we derived.