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)
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)
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Let's use x as the number of minutes it takes for the machines to fill the same number of cans.
For the first machine, the number of cans filled is given by 180 + 15x (180 cans filled initially and then 15 cans per minute).
For the second machine, the number of cans filled is given by 210 + 12x (210 cans filled initially and then 12 cans per minute).
To find when the two machines will have filled the same number of cans, we can set these two expressions equal to each other:
180 + 15x = 210 + 12x
Let x represent the number of minutes it takes for the two machines to have filled the same number of cans of soup.
For the first machine, the number of cans filled can be represented as 180 + 15x.
For the second machine, the number of cans filled can be represented as 210 + 12x.
Since we want the two machines to have filled the same number of cans of soup, we can set up the following equation:
180 + 15x = 210 + 12x
To find the equation that represents when the two machines will have filled the same number of cans of soup, we can use the equation for each machine's total cans filled.
For the first machine, the equation is:
Total cans filled by first machine = 180 + 15x
For the second machine, the equation is:
Total cans filled by second machine = 210 + 12x
Since we want to find the point at which both machines have filled the same number of cans, we can set these two equations equal to each other:
180 + 15x = 210 + 12x
Now we can solve this equation to find the value of x, which represents the time (in minutes) it takes for the two machines to fill the same number of cans of soup.