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)

Question

Responses

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

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

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

92−16x=104−13x
; x=−4

Answer 1

To find when the two machines will have filled the same number of cans, we can set up the following equation:

1. The first machine has filled 92 cans and fills 16 cans per minute, so after \( x \) minutes, it will have filled \( 92 + 16x \) cans.
2. The second machine has filled 104 cans and fills 13 cans per minute, so after \( x \) minutes, it will have filled \( 104 + 13x \) cans.

We want to find \( x \) when both machines have filled the same number of cans:

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

Now, let's solve for \( x \):

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

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

\[ 92 + 3x = 104 \]

2. Subtract 92 from both sides:

\[ 3x = 104 - 92 \]

\[ 3x = 12 \]

3. Divide by 3:

\[ x = 4 \]

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

The correct response is: 92 + 16x = 104 + 13x ; x = 4.