Can you help me understand this student's method for problem #3?

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The discussion centers on understanding a student's reasoning for problem #3, where her method seems unclear despite arriving at the correct answer. The original poster finds the student's approach puzzling and suggests that it would be more logical to directly calculate the average by adding the fifth score to the original four and dividing by five. Both methods yield the same result, highlighting that the difference lies in the process rather than the outcome. The poster expresses difficulty in explaining the student's reasoning beyond reiterating the mathematical steps involved. Ultimately, the focus is on the distinction between different problem-solving approaches.
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can someone help me out on #3 please. I can't see the reasoning behind her work.
 

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Her reasoning would make more sense if you jumped straight to answering b).
 
I did look at b and her math is correct but it's the reasoning that I am not seeing. I would have just taken the original 4 scores, added the fifth score, and divided by 5.
 
Obviously both your method and hers are equivalent since they're both correct, but the process which is used is the only difference. It's somewhat similar to solving 5-2 by first starting with 5 and then taking away 2 as compared to solving -2+5 which is to first start with -2.

All I could do in explaining her reasoning would be to repeat exactly what the maths tells you.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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