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) Responses 12x+180=15x+210 12 x plus 180 equals 15 x plus 210 12x−210=15x−180 12 x minus 210 equals 15 x minus 180 210−12x=180−15x 210 minus 12 x equals 180 minus 15 x 12x+210=15x+180

Answer 1

To find when the two machines will have filled the same number of cans of soup, we can set up equations for the total number of cans filled by each machine as a function of time, \( x \) (in minutes).

For the first machine:

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

For the second machine:

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

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

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

So, the correct equation to show when the two machines will have filled the same number of cans of soup is:

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

In your answer choices, that matches:

Response: 12x + 180 = 15x + 210