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 2 as your
variable. (1 point)
wrong
Let's use 't' as the variable to represent time in minutes.
To find the equation, we need to determine when the total number of cans filled by each machine will be the same.
The first machine fills cans at a rate of 15 per minute, so its equation can be represented as:
Cans filled by the first machine = 180 + 15t
The second machine fills cans at a rate of 12 per minute, so its equation can be represented as:
Cans filled by the second machine = 210 + 12t
Now, we want to find the time when the two machines will have filled the same number of cans, which means the two equations will be equal.
So, we can set up the equation:
180 + 15t = 210 + 12t
Simplifying the equation:
15t - 12t = 210 - 180
3t = 30
Dividing both sides of the equation by 3:
t = 10
Therefore, the equation to show when the two machines will have filled the same number of cans of soup is:
180 + 15t = 210 + 12t, where t = 10.
Let's assume that the number of minutes it takes for the two machines to fill the same number of cans is represented by the variable "x".
For the first machine, the number of cans filled can be represented by the equation: 180 + 15x.
For the second machine, the number of cans filled can be represented by the equation: 210 + 12x.
To find when the two machines will have filled the same number of cans, we can set the two equations equal to each other and solve for x:
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.
The first machine fills 15 cans of soup per minute, so after x minutes it will have filled 15x cans of soup.
The second machine fills 12 cans of soup per minute, so after x minutes it will have filled 12x cans of soup.
Since we want to find when the two machines will have filled the same number of cans of soup, we can set up the equation 15x = 12x.
Therefore, the equation to show when the two machines will have filled the same number of cans of soup is 15x = 12x.