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 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 the two machines will have filled the same number of cans of soup, we can set up the equation based on the number of cans each machine has filled over time.

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

The first machine has already filled 92 cans and fills at a rate of 16 cans per minute, so the total number of cans filled by the first machine after \( x \) minutes is: \[ 92 + 16x \]

The second machine has already filled 104 cans and fills at a rate of 13 cans per minute, so the total number of cans filled by the second machine after \( x \) minutes is: \[ 104 + 13x \]

To find when both machines have filled the same number of cans, we set the two expressions equal to each other: \[ 92 + 16x = 104 + 13x \]

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

1. Subtract \( 13x \) from both sides: \[ 92 + 3x = 104 \]

2. Subtract 92 from both sides: \[ 3x = 12 \]

3. Divide both sides by 3: \[ x = 4 \]

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

Conclusion

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

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