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

Question

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

Answer 1

Let x be the number of minutes it takes for the two machines to fill the same number of cans of soup.

The number of cans of soup the first machine fills in x minutes is 15x.
The number of cans of soup the second machine fills in x minutes is 12x.

To find the equation, we set up the equation 180 + 15x = 210 + 12x, since the total number of cans filled by each machine and the respective rates of filling must be equal.

Simplifying the equation, we get:

180 + 15x = 210 + 12x

Subtracting 12x from both sides, we get:

3x = 30

Dividing both sides by 3, we get:

x = 10

Therefore, the equation is x = 10, representing that it takes 10 minutes for the two machines to fill the same number of cans of soup.

Answer 2

Let's assume that the number of minutes needed for the two machines to have filled the same number of cans of soup is x.

The total number of cans filled by the first machine after x minutes is 180 + 15x.

The total number of cans filled by the second machine after x minutes is 210 + 12x.

To find when the two machines will have filled the same number of cans of soup, we can set up the equation:

180 + 15x = 210 + 12x.

Now, we can solve this equation for x. Subtracting 12x from both sides of the equation gives:

3x = 30.

Finally, dividing both sides of the equation by 3 gives:

x = 10.

Therefore, the two machines will have filled the same number of cans of soup after 10 minutes.

Answer 3

To find the time when the two machines will have filled the same number of cans of soup, we can set up an equation.

Let x be the number of minutes passed.

For the first machine, the total number of cans filled in x minutes can be calculated as 180 + 15x (since it fills 15 cans per minute and already filled 180 cans).

For the second machine, the total number of cans filled in x minutes can be calculated as 210 + 12x (since it fills 12 cans per minute and already filled 210 cans).

To find the time when both machines have filled the same number of cans, we can set up the equation:

180 + 15x = 210 + 12x

Simplifying this equation further will give us the solution.