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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 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 12 x plus 180 equals 15 x plus 210 Skip to navigation

1 answer

To set up the equation for when the two machines will have filled the same number of cans of soup, we need to consider how many cans each machine will have filled after \( x \) minutes.

  1. The first machine has already filled 180 cans and fills at a rate of 15 cans per minute. After \( x \) minutes, the number of cans filled by the first machine will be: \[ \text{Cans filled by first machine} = 180 + 15x \]

  2. The second machine has already filled 210 cans and fills at a rate of 12 cans per minute. After \( x \) minutes, the number of cans filled by the second machine will be: \[ \text{Cans filled by second machine} = 210 + 12x \]

Now, we want to find \( x \) when both machines have filled the same amount of soup. Thus, we set the two equations equal to each other: \[ 180 + 15x = 210 + 12x \]

This is the equation that represents when both machines will have the same number of soup cans filled.

Now, looking at the provided responses:

  • The closest option to the equation we derived is 12x + 210 = 15x + 180.

So this response is correct.