Mr. Lai’s Math Blog

student tutorials on math contest questions

1998 Question #23 (by Katherine B., Kathryn N.)

Posted by elai on October 17, 2008




10 Responses to “1998 Question #23 (by Katherine B., Kathryn N.)”

  1.   Aman Basra Says:

    It was really simple and easy to understand. I especially found the diagrams helpful.

  2.   Valerie Leung Says:

    The solution was easy to understand although it took me awhile to figure out where you got 2x from. Good job.

  3.   elai Says:

    Aman. Did the diagrams help clarify something SPECIFIC about the problem?

  4.   christine pennington Says:

    i watched this a few times adn i’m still not sure where the 2x came from. other then that you made the problem really easy to follow. i liked the diagram; it helped me to visualize the problem, and figure out which areas corresponded to which portions of the rugs.

  5.   Roxanne Henschke Says:

    I thought the diagram was helpful to understanding the problem. But, I also can’t figure out where you got 2x from.

  6.   Aman Basra Says:

    to clarify what i meant about the diagram, when I first read the question it was kind of hard to comprehend the problem in my mind as I couldn’t visualize the set up of the carpets. The idea of circles overlapping especially demonstrates the layout of the overlapping really well.

  7.   Shelly Liu Says:

    The solution is well explained and the explanation is clear.
    Someone mention about where does the 2x come from and i have the same question for that
    I don’t understand why is it 2x instead of x
    If the totally area of the over lapping part were a,b,c,x and their sum was equal to 60, then the equation should be a+b+c+x=60
    The 2x would double the middle area.
    Is it because the x area is triple layer or the 2 has other meaning?

  8.   Henry Fang Says:

    It was well explained and the diagram really helped me visualized the problem.
    but i have the same question as many others had. Where did the 2X come from which is part of the equation a+b+c+2x=60. I tried to figure out myself but still don’t know why is that. Other then this problem, i got the rest of the explanations. Well done!!!

  9.   Solomon Vandt Says:

    First of all, slowing down the whole explanation would have made me better comprehend the solution. It was all a blur to me the first time I watched it.

    I didn’t get that a+b+c+2x=60 part because of the 2x as well. Why was it not x instead of 2x?

    The diagram also really helped me visualize the problem, which helped me understand the solution better.

  10.   Esther Tung Says:

    This question is explained in a very simple manner, which is very good. However, the audio guide is WAY TOO FAST. The entire video is 37 seconds long- too short a time for the brain to process everything. It took me 10 minutes of pausing and pondering over the a+b+c+2x=60 part before I understood it why it was 2x instead of just x. It would have been really helpful if you could have explained it little.

    And to answer the mutual question of the above people, this is how the 2x came to be:

    *refer to diagram*:

    Mat Red is on the very bottom therefore its entire area is on the ground and is not overlapping anything.

    Mat Blue is on top of Mat Red, therefore the areas b+x is overlapping Mat Red.

    Mat Yellow is on the very top, overlapping both Mat Red and Mat Blue. The mat is overlapping Mats Red and Blue at areas a+x+c.

    To sum it up, mat Red does not overlap anything, mat Blue overlaps Red at b+x, and mat Yellow overlaps mats Red and Blue at a+x+c. If you add all the areas that are overlapped on EVERY MAT, you will get (b+x)+(a+x+c)=60, or a+b+c+2x=60, and voila!

    P.S. The diagram was really really helpful, I must say! The colours reallly aided me in visualizing the situation with the overlapping and understand how the 2x came to be. Good job!

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