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
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
To find out when the two machines will have filled the same number of cans of soup, we can set up an equation.
Let's say it takes x minutes for the first machine to fill the same number of cans as the second machine. So, in x minutes, the first machine would have filled 15x cans of soup, and the second machine would have filled 12x cans of soup.
The equation can be written as:
180 + 15x = 210 + 12x
Here's how we get there:
The first machine has already filled 180 cans of soup. So, after x minutes, it would have filled 15x cans.
The second machine has already filled 210 cans of soup. So, after x minutes, it would have filled 12x cans.
By setting the two quantities equal to each other, we find when they will have filled the same number of cans. Adding the initial number of cans filled by each machine on both sides of the equation ensures we have a balanced equation.
Now, we can solve this equation to find the value of x, which represents the number of minutes it will take for the two machines to reach the same number of filled cans.
Let's assume that it takes x minutes for the two machines to fill the same number of cans of soup.
The first machine fills cans at a rate of 15 per minute, so in x minutes it will fill 15x cans of soup.
The second machine fills cans at a rate of 12 per minute, so in x minutes it will fill 12x cans of soup.
To find when the two machines will have filled the same number of cans of soup, we can set the two expressions equal to each other:
15x = 12x + 30
Simplifying the equation, we get:
3x = 30
Dividing both sides by 3, we get:
x = 10
Therefore, it will take 10 minutes for the two machines to fill the same number of cans of soup.