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
210−12x=180−15x
210 minus 12 x equals 180 minus 15 x
12x+210=15x+180
12 x plus 210 equals 15 x plus 180
12x−210=15x−180
12 x minus 210 equals 15 x minus 180
12x+180=15x+210
12 x plus 180 equals 15 x plus 210
210 - 12x = 180 - 15x
The equation to show when the two machines will have filled the same number of cans of soup is:
12x + 210 = 15x + 180
To write an equation to show when the two machines will have filled the same number of cans of soup, we can set the number of cans filled by the first machine equal to the number of cans filled by the second machine.
Let x be the number of minutes it takes for the first machine to fill the cans.
The first machine fills cans at a rate of 12 per minute, so the number of cans filled by the first machine after x minutes is 12x.
The second machine starts with 210 cans already filled and fills cans at a rate of 15 per minute. So the number of cans filled by the second machine after x minutes would be 210 + 15x.
Therefore, the equation to show when the two machines will have filled the same number of cans of soup is:
12x = 210 + 15x
Simplifying further, we have:
12x - 15x = 210
-3x = 210
Divide both sides of the equation by -3:
x = 210/-3
x = -70
Therefore, the two machines will have filled the same number of cans of soup after -70 minutes, which doesn't make sense in this context. So, it may mean that there is an error in the information provided.