Question

Two machines at a factory are filling cans of soup. One machine has filled 92 cans of soup. It fills cans at a rate of 16 cans per minute. The second machine has filled 104 cans of soup. It fills cans at a rate of 13 cans per minute. Write and solve an equation to show when the two machines will have filled the same number of cans of soup.(1 point)
Responses

104+16x=92+13x
; x=4
104 plus 16 x equals 92 plus 13 x ; x equals 4

92+16x=104+13x
; x=6
92 plus 16 x equals 104 plus 13 x ; x equals 6

92−16x=104−13x
; x=−4
92 minus 16 x equals 104 minus 13 x ; x equals negative 4

92+16x=104+13x
; x=4

Answer 1

To determine when the two machines will have filled the same number of cans of soup, we can set up the equation based on their rates and the cans they've already filled.

Let \(x\) be the number of minutes that have passed.

- The first machine starts with 92 cans and fills at a rate of 16 cans per minute, so after \(x\) minutes, it will have filled \(92 + 16x\) cans.
- The second machine starts with 104 cans and fills at a rate of 13 cans per minute, so after \(x\) minutes, it will have filled \(104 + 13x\) cans.

To find when both machines have filled the same number of cans, we can set these two expressions equal to each other:

\[
92 + 16x = 104 + 13x
\]

Now, we can solve this equation for \(x\):

1. Subtract \(13x\) from both sides:

\[
92 + 16x - 13x = 104
\]

This simplifies to:

\[
92 + 3x = 104
\]

2. Next, subtract 92 from both sides:

\[
3x = 104 - 92
\]

This simplifies to:

\[
3x = 12
\]

3. Finally, divide both sides by 3:

\[
x = 4
\]

So, the correct response is:

\(104 + 16x = 92 + 13x\) ; \(x = 4\)

Thus, after 4 minutes, both machines will have filled the same number of cans of soup.