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

12x+180=15x+210
12x+210=15x+180
210-12x=180-15x
12x-210=15x-180

Answer 1

To find when the two machines have filled the same number of cans, we need to set up an equation that compares the total number of cans each machine has filled over time.

• Let \( x \) represent the time in minutes after the current state.
• The first machine has already filled 180 cans and fills at a rate of 15 cans per minute. Therefore, the total number of cans filled by the first machine after \( x \) minutes will be \( 15x + 180 \).
• The second machine has already filled 210 cans and fills at a rate of 12 cans per minute. Therefore, the total number of cans filled by the second machine after \( x \) minutes will be \( 12x + 210 \).

Setting these two expressions equal to each other gives us the equation:

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

This is the correct equation to show when the two machines will have filled the same number of cans of soup. If you need to solve for \( x \) or analyze it further, let me know!