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

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

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

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

Answer 1

To find out when both machines will have filled the same number of cans of soup, we can set up the following equation.

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

For the first machine:

• It has already filled 92 cans and fills at a rate of 16 cans per minute. So, after \( x \) minutes, it will have filled: \[ 92 + 16x \]

For the second machine:

• It has already filled 104 cans and fills at a rate of 13 cans per minute. So, after \( x \) minutes, it will have filled: \[ 104 + 13x \]

We want to find when these two amounts are equal: \[ 92 + 16x = 104 + 13x \]

Now we can 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: \[ x = 4 \]

Therefore, the correct equation is: \[ 92 + 16x = 104 + 13x \] And the solution is: \[ x = 4 \]

So, the correct response is: 92 + 16x = 104 + 13x ; x = 4.