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

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

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 an equation based on the number of cans each machine has filled over time.

The first machine has already filled 92 cans and continues to fill at a rate of 16 cans per minute. Therefore, after \( x \) minutes, the total number of cans filled by the first machine will be:

\[ 92 + 16x \]

The second machine has already filled 104 cans and continues to fill at a rate of 13 cans per minute. Therefore, after \( x \) minutes, the total number of cans filled by the second machine will be:

\[ 104 + 13x \]

We want to find when both machines will have filled the same number of cans:

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

Now, we can solve the equation:

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:

\[ x = \frac{12}{3} \]

So,

\[ x = 4 \]

Therefore, the correct equation is \( 92 + 16x = 104 + 13x \) and the solution is \( x = 4 \). The answer is:

\[ 92 + 16x = 104 + 13x ; ; ; x = 4 \]