Question

Two machines at a factory are filling cans up of soup one machine filled 92 cans of soup 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 per minute. Write and solve an equation to show when the two machines will have filled the same number of cans
104+16x=92+13x ; x=4
92+16x=104+13x ; x=4
92-16x=104-13x ; x=-4
92+16x=104+13x ;x=6

Answer 1

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

Let's denote \( x \) as the number of minutes after the observation.

1. The first machine initially filled 92 cans and fills at a rate of 16 cans per minute. Therefore, after \( x \) minutes, the total number of cans it has filled will be:
\[
92 + 16x
\]

2. The second machine initially filled 104 cans and fills at a rate of 13 cans per minute. Therefore, after \( x \) minutes, the total number of cans it has filled will be:
\[
104 + 13x
\]

Now we want to find when the two machines have filled the same number of cans. We set these two expressions equal to each other:
\[
92 + 16x = 104 + 13x
\]

Next, we can solve the equation:

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

So, the two machines will have filled the same number of cans after **4 minutes**. The correct equation and solution is:

**Equation**: \( 92 + 16x = 104 + 13x \)

**Solution**: \( x = 4 \)