Linear Equations in Real-World Scenarios Quick Check
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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 plus 16 x equals 104 plus 13 x, ; , x equals 4
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 minus 16 x equals 104 minus 13 x, ; , x equals negative 4
92+16x=104+13x ; x=6
The correct equation is 92 + 16x = 104 + 13x, where x represents the number of minutes.
To solve for x, we can simplify the equation by subtracting 92 from both sides:
16x = 12 + 13x
Then, we can subtract 13x from both sides:
3x = 12
Finally, we can solve for x by dividing both sides by 3:
x = 4
Therefore, the two machines will have filled the same number of cans of soup after 4 minutes.
The correct response is: 92 plus 16 x equals 104 plus 13 x, ; , x equals 4.
To solve the problem, we need to set up an equation that shows when the two machines will have filled the same number of cans of soup.
Let's use the variables x for the time in minutes and y for the number of cans filled.
For the first machine, we know that it has already filled 92 cans and fills cans at a rate of 16 cans per minute. So, the equation for the cans filled by the first machine is y = 92 + 16x.
For the second machine, we know that it has already filled 104 cans and fills cans at a rate of 13 cans per minute. So, the equation for the cans filled by the second machine is y = 104 + 13x.
To find when the two machines will have filled the same number of cans, we need to solve the equations for y.
Setting the two equations equal to each other, we get:
92 + 16x = 104 + 13x
Now, let's solve this equation to find the value of x. Subtracting 13x from both sides gives:
3x = 12
Dividing both sides by 3 gives:
x = 4
So, the two machines will have filled the same number of cans after 4 minutes.
The correct response is: 92 + 16x = 104 + 13x ; x = 4
The correct equation to show when the two machines will have filled the same number of cans of soup is:
92 + 16x = 104 + 13x
To solve this equation, we want to isolate the variable x. We do this by subtracting 13x from both sides of the equation:
92 + 16x - 13x = 104
Combine like terms:
3x + 92 = 104
Next, we want to isolate the variable x by subtracting 92 from both sides of the equation:
3x + 92 - 92 = 104 - 92
3x = 12
Finally, we solve for x by dividing both sides of the equation by 3:
x = 4
Therefore, the two machines will have filled the same number of cans of soup after 4 minutes.