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) Responses 12x+210=15x+180 12 x plus 210 equals 15 x plus 180 12x+180=15x+210 12 x plus 180 equals 15 x plus 210 210−12x=180−15x 210 minus 12 x equals 180 minus 15 x 12x−210=15x−180

Answer 1

To find out when the two machines will have filled the same number of cans of soup, we need to set up the equations for the total number of cans filled by each machine based on the time (in minutes) they operate.

Let \( x \) represent the number of minutes.

The first machine, which has already filled 180 cans at a rate of 15 cans per minute, will fill:
\[
180 + 15x
\]

The second machine, which has already filled 210 cans at a rate of 12 cans per minute, will fill:
\[
210 + 12x
\]

We want to find when these two quantities are equal:
\[
180 + 15x = 210 + 12x
\]

To simplify, we can move \( 12x \) to the left and 180 to the right:
\[
15x - 12x = 210 - 180
\]
This simplifies to:
\[
3x = 30
\]
Dividing both sides by 3:
\[
x = 10
\]

This means that after 10 minutes, both machines will have filled the same number of cans.

**The correct equation to set up is:**
\[
180 + 15x = 210 + 12x
\]
You can choose from the given responses, but it matches the first one you provided:
\[
15x + 180 = 12x + 210
\]
In simplified terms, it's the same as the equation derived above.