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.(1 point)

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.(1 point)

Answer 1

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Answer 2

The equation to show when the two machines will have filled the same number of cans of soup is:

180 + 15x = 210 + 12x

where x is the number of minutes it will take for the two machines to fill the same number of cans of soup.

Answer 3

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.

2x+210=15x+180

210−12x=180−15x

12x+180=15x+210

12x−210=15x−180

Answer 4

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Answer 5

To write the equation that represents when the two machines will have filled the same number of cans, we need to consider the initial number of cans filled and the respective rates at which each machine fills cans.

Let's start with the machine that has already filled 180 cans. To represent the number of cans filled by this machine, we can use the equation:

Cans_filled_by_machine_1 = 180 + 15x

Here, x represents the time in minutes.

Similarly, for the second machine that has already filled 210 cans, we can use the equation:

Cans_filled_by_machine_2 = 210 + 12x

The equation we need is the one where both machines have filled the same number of cans. To express this, we set the two equations equal to each other:

180 + 15x = 210 + 12x

By subtracting 12x from both sides, we get:

180 + 15x - 12x = 210

Combining like terms, we simplify to:

3x = 210 - 180

Further simplifying:

3x = 30

Now, we divide both sides by 3 to solve for x:

x = 30/3

x = 10

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