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

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

Answer 1

To find out when the two machines will have filled the same number of cans, we can set up the equations based on the information given.

Let's denote \(x\) as the number of minutes that will pass.

For the first machine:
- It has already filled 92 cans and fills at a rate of 16 cans per minute.
- After \(x\) minutes, it will have filled \(92 + 16x\) cans.

For the second machine:
- It has already filled 104 cans and fills at a rate of 13 cans per minute.
- After \(x\) minutes, it will have filled \(104 + 13x\) cans.

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

Now we can solve this equation.

1. Start by moving the \(13x\) from the right side to the left side:
\[
92 + 16x - 13x = 104
\]
\[
92 + 3x = 104
\]

2. Next, subtract 92 from both sides:
\[
3x = 104 - 92
\]
\[
3x = 12
\]

3. Now, divide both sides by 3:
\[
x = 4
\]

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

Thus, the correct response is:
\[
92 + 16x = 104 + 13x; \quad x = 4
\]