Two machines at a factory are filling cans of soup one machine has already filled 180 cans of soup and fill cans at a rate of 15 per minute the second machine has already filled 210 cans of soup and fill cans at a rate of 12 per minute write an equation to show 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 fill cans at a rate of 15 per minute the second machine has already filled 210 cans of soup and fill cans at a rate of 12 per minute write an equation to show the two machines will have filled the same number of cans of soup use X as your variable.

Answer 1

The equation to show the two machines will have filled the same number of cans of soup can be written as:

180 + 15X = 210 + 12X

Answer 2

Let's use X as the variable representing the number of minutes it takes for both machines to fill the same number of cans of soup.

The first machine fills cans at a rate of 15 cans per minute, so after X minutes, it will have filled 15X cans of soup.

The second machine fills cans at a rate of 12 cans per minute, so after X minutes, it will have filled 12X cans of soup.

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

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

To find the equation that shows the two machines will have filled the same number of cans of soup after X minutes, we set the two expressions equal to each other:

180 + 15X = 210 + 12X

Now we can solve for X.

Answer 3

To write an equation that shows the two machines will have filled the same number of soup cans, we need to equate the total number of cans filled by each machine.

Let's assume that after X minutes, both machines will have filled the same number of cans.

The first machine fills cans at a rate of 15 per minute, so after X minutes, it will have filled 15X cans.

Similarly, the second machine fills cans at a rate of 12 per minute, so after X minutes, it will have filled 12X cans.

To equate the two machines' cans filled, we can write the equation:

15X = 12X

This equation states that the number of cans filled by the first machine (15X) is equal to the number of cans filled by the second machine (12X).

Simplifying this equation, we can subtract 12X from both sides:

15X - 12X = 12X - 12X

Simplifying further:

3X = 0

Therefore, we have determined that the two machines will have filled the same number of cans when X = 0.

Please note that this equation does not have a unique solution, as there are multiple values of X that satisfy the equation and represent the time it takes for the machines to fill the same number of cans.