Linear Equations in Real-World Scenarios Quick Check

Question

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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 minus 16 x equals 104 minus 13 x ; x equals negative 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 plus 16 x equals 104 plus 13 x ; x equals 4

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

Answer 1

To determine when both machines will have filled the same number of cans of soup, we can set up the equations based on the information provided.

Let \( x \) represent the number of minutes that have passed since the machines started filling the cans.

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

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

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

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

Thus, the correct response from the options given would be: 92 + 16x = 104 + 13x; x = 4.