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

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

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

210−12x=180−15x

Answer 1

To determine when the two machines will have filled the same number of cans of soup, we need to write an equation that captures the total number of cans filled by each machine over time.

Let \( x \) be the number of minutes after the start point.

• The first machine starts with 180 cans and fills at a rate of 15 cans per minute, so the expression for the total number of cans filled by the first machine is:
  \( 180 + 15x \).

• The second machine starts with 210 cans and fills at a rate of 12 cans per minute, so the expression for the total number of cans filled by the second machine is:
  \( 210 + 12x \).

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

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

Now, looking at your response options, this corresponds to:

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

So, the correct equation is:

12x + 210 = 15x + 180.