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
Let x represent the number of minutes it takes for the two machines to have filled the same number of cans of soup.
The number of cans filled by the first machine after x minutes is 180 + 15x.
The number of cans filled by the second machine after x minutes is 210 + 12x.
Since we want the two machines to have filled the same number of cans of soup, we can set the two expressions equal to each other and solve for x:
180 + 15x = 210 + 12x
Let's assume x represents the time in minutes.
The number of cans filled by the first machine at time x is given by 180 + 15x.
The number of cans filled by the second machine at time x is given by 210 + 12x.
To find when the two machines will have filled the same number of cans, we need to set these expressions equal to each other and solve for x.
180 + 15x = 210 + 12x
Subtracting 12x from both sides:
3x = 30
Dividing both sides by 3:
x = 10
Therefore, the two machines will have filled the same number of cans after 10 minutes.