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.
2x+210=15x+180
210−12x=180−15x
12x+180=15x+210
12x−210=15x−180
12x + 180 = 15x + 210
The equation that shows when the two machines will have filled the same number of cans of soup is:
12x + 180 = 15x + 210
To write an equation to show when the two machines will have filled the same number of cans of soup, let's use the variable x to represent the number of minutes it takes for the two machines.
First, let's consider the number of cans filled by the first machine. The machine has already filled 180 cans of soup, and it fills cans at a rate of 15 per minute. Therefore, the total number of cans filled by the first machine after x minutes is given by 15x.
Now let's consider the number of cans filled by the second machine. The machine has already filled 210 cans of soup, and it fills cans at a rate of 12 per minute. Therefore, the total number of cans filled by the second machine after x minutes is given by 12x.
The equation to show when the two machines will have filled the same number of cans of soup is:
15x = 12x + 210
In this equation, we set the number of cans filled by the first machine (15x) equal to the number of cans filled by the second machine (12x) plus the initial number of cans filled by the second machine (210).
Simplifying the equation, we have:
15x - 12x = 210
This equation represents the point in time when the two machines will have filled the same number of cans of soup.