Linear Equations in Real-World Scenarios Quick Check

Question

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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

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

Answer 1

To determine when the two machines will have filled the same number of cans of soup, we need to express the total number of cans filled by each machine as a function of time (in minutes), using \( x \) as the number of minutes after the given amounts.

1. For the first machine:

   • It has already filled 180 cans and fills at a rate of 15 cans per minute.
   • The total number of cans filled after \( x \) minutes is \( 180 + 15x \).

2. For the second machine:

   • It has already filled 210 cans and fills at a rate of 12 cans per minute.
   • The total number of cans filled after \( x \) minutes is \( 210 + 12x \).

Now, to find out when the two machines will have filled the same number of cans, we set their total filled equations equal to each other:

\[ 180 + 15x = 210 + 12x \]

We can rearrange to isolate \( x \).

However, looking at the options provided, the correct mathematical representation is:

\[ 15x + 180 = 12x + 210 \]

So, the correct choice is:

12x + 210 = 15x + 180