The Art Of Problem Solving!!!

Discussion in 'Math' started by steeve_wai, Sep 22, 2007.

  1. steeve_wai

    Thread Starter Active Member

    Sep 13, 2007
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    0
    mobile recharge cards of 100(a) and 109(b) give a talktime of 91 and 100 respectively.which one is BETTER?

    the ANSWER TO THIS QUESTION IS NOT IMPORTANT,THE WAY YOU SOLVE THIS PROBLEM MATTERS.anyway...READ WHAT FOLLOWS ONLY AFTER YOU SOLVE THIS PROBLEM YOURSELF...


















































































































    now,
    consider a ratio p/q, p<q, p>0,q>0.
    addition of a POSITIVE constant,say m, to the numerator(N) and to the denominator(D) gives a ratio greater or lesser than the ratio we started with?


    possible approaches:

    1)subtract one ratio from the other and see if the result is positive or not.(NOT GOOD)

    2)MY APPROACH: I WILL USE AN EXAMPLE TO ILLUSTRATE IT:

    SYSTEM X SYSTEM Z
    6/7 ? 11/12. (=(6+5)/(7+5))

    observe that N-D is 1 for both the ratios.
    so,for system z we get a HIGHER OUTPUT for the COMMON LOSS OF 1.
    hence system z is better,HENCE 11/12 > 6/7.


    answer to the main problem: for a service charge of 9, offer 'b' is better than offer 'a'.


    ANOTHER ONE THAT I SAW IN DAILY LIFE:

    i want to photocopy 32 pages. each page costs 0.75. how much do i have to pay.YOU DONT HAVE TO THINK MUCH.

    0.75 is 3/4. and (3/4) * 32 is 24.

    MORAL OF THE STORY: THE SOLUTION TO A PROBLEM DEPENDS ON HOW YOU LOOK AT IT.please comment on my article. add any similar problems if you can...i will be very grateful if you do so.
    THANK YOU FOR READING PATIENTLY...god bless us all...
     
  2. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
    6
    I am reminded of a penny-pinching Welshman living in the hills above Coquille Oregon. He prefers to use 3 watt 80 lumen LED floods to using 9 watt 500 lumen CF bulbs. The CFs are clearly more efficient at converting electricity into light (56 lumen per watt vs 27 lumen per watt). BUT the LEDs last ten times as long while costing only 7.5 times as much. Also, the Welchman in question claims that excess light from the CFs is simply wasted - he claims to need only 50 or 60 lumens to read by!:D
     
  3. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Often the question is price per unit, and this is ultimately what you are representing with your ratioed argument. The question you then must ask is raised by thingmaker3's post - what do you need.

    Consider a typical broadband package with download limits:

    1) Pay £25 for an unlimited service per month
    2) Pay £15 for a limited service of 10GB per month

    Option 1) clearly gives you better download levels per pound spent, but if you don't download more than 10GB per month then you would waste £10 per month.

    Dave
     
  4. steeve_wai

    Thread Starter Active Member

    Sep 13, 2007
    47
    0
    are you saying that i am spending more in the offer that is more BENEFICIAL...true,you spend more and get more talktime for the fixed price of 9...i was only talking about the benifit,and not HOW MUCH YOU NEED...obviously if you only have 100 to spend how will you buy the card that costs 109 even though its better
     
  5. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    There is a difference between not being able to buy something, and not needing to buy something. The first is a forced decision whether it is the best for you or not, and the second is decision based on benefit and need. One has choice, the other does not.

    Dave
     
  6. recca02

    Senior Member

    Apr 2, 2007
    1,211
    0
    i concur with Mr Dave here,
    the question was which one is better and the answer to that is objective oriented.
    this is what those wily scheming men in black (read managers) come up with to maximize profit.
     
  7. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Indeed it is the same principle as the "buy two get a third free" or "buy one and get a second half price" - the idea is to make you buy more than you need. Actually there is a further to this in that buy shifting more units of an item (even at a reduced cost) they are turning stock over quicker which allows them to buy bulk and reduce the cost at source.

    Dave
     
  8. steeve_wai

    Thread Starter Active Member

    Sep 13, 2007
    47
    0
    yes, dave, what you say is true.YOU PAY MORE AND "GET" MORE.i hope that the problem helped us to see things in a different ,maybe better way...thank you for replying...your opinions are valuable...
     
  9. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    A final point I will make in all this is the issue of confidence - this is particularly important in the world of macro-economics. By shifting larger quantities of a product, even at a reduced price, you breed confidence in your market and customers. From this increased confidence it is easier to convince consumers to buy into a 'better' deal - people feel they need more than they do, and at this point value is no longer in the eye of the beholder (as before) but in the message portrayed by the manufacturer. We getting well off topic with your original point, but these issues are all interrelated.

    Dave
     
  10. steeve_wai

    Thread Starter Active Member

    Sep 13, 2007
    47
    0
    consider this,
    think of ratios as,say a machine that takes energy as an input and gives work as output,both in joules.system x gives 6 for an input of 7.system z gives 11 for an input of 12.the LOSS is the same.SO WHICH machine is "better".ofcourse,if i want to do only 6 joules of work,why should i take system z,and end up spending more...try to look at the mathematics only and not the business related aspects...those aspects are of importance in the real world and not in theoretical discussions such as these...
     
  11. thingmaker3

    Retired Moderator

    May 16, 2005
    5,072
    6
    I have an old copy of Esbach's reference for engineers. The very first section deals with keeping the employer's economics in mind.

    Do they still teach this?
     
  12. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
    144
    Very much so. In my undergraduate and postgraduate degrees the subject of economics was taught as a separate module of economics, covering both micro and macro. It is also widely covered as part of Systems Engineering courses.

    Dave
     
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