Please Explain this Mathematicians

1. 89

   mistyhorizon2003posted 13 years ago

   Okay, just heard this on a TV programme/documentary, but sadly missed the crucial solution. It is now bugging me no end, I just can't explain it, so I need someone, anyone in fact, to explain to me how this works. Here goes:
   
   3 friends go to a restaurant for a meal.
   
   The bill arrives and it is for £25.
   
   Each of them put £10 on to the waiter's dish.
   
   The waiter brings them back 5 x £1 coins in change.
   
   Each of the 3 friends keeps £1 of the change for themselves, leaving the waiter with the remaining £2.
   
   This means that each person paid £10 for their meal, less £1 they took as change = £9 for their meal.
   
   3 friends x £9 per meal = £27
   
   The waiter took the £2 change left in the dish.
   
   £27 paid by the friends for their meal + £2 tip for the waiter = £29.
   
   What happened to the missing £1, bearing in mind each person put down £10 initially, totalling £30, NOT £29
   
   Help, this is driving me mad.

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   1. 0

      andycoolposted 13 years agoin reply to this

      So simple... 3 friends paid $10 each... that equals $10*3=$30.
      The waiter brought back $5... of which each of the three took $1. That means they individually spent $9 for paying the bill plus to the waiter. $9*3 = $27. $3 remained... which is their money of $1 each which they took. $2 was given to the waiter in which everyone paid $2 / 3 = $0.67 each and $25/3 = $8.33 was paid individually by them for meal.
      
      So the final equation is:
      Payment for meal per head=$8.33
      Payment to the waiter per head=$0.67
      Total payment per head = $8.33 + $0.67 = $9
      
      They paid in gross =                     $30
      Total net payment =          $9*3 =$27
      Subtract (-)
      ____________________________
      Money left                                      = $3           
      Of which they took   $1 per head.

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   2. 75

      Mikel G Robertsposted 13 years agoin reply to this

      Which already includes the tip, leaving only the 3 that they each retrieved.

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      1. 0

         andycoolposted 13 years agoin reply to this

         Yeah... that's the fallacy!

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2. 60

   paradigmsearchposted 13 years ago

   Each of the 3 persons put down 10 and took back 1. Which equals 27.
   
   In other words, each of the 3 persons put down a net of 9. Which equals 27.
   
   25 for the meal, plus 2 left for the waiter. Which equals 27.

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   1. 89

      mistyhorizon2003posted 13 years agoin reply to this

      Still confused, £30 was put down in total, £2 went to the waiter as a tip, leaving £28. Each friend had paid £9 allowing for the change they received, i.e. £27. £27 + £2 = £29, not £30, so where is the missing £1???

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3. 89

   mistyhorizon2003posted 13 years ago

   Blow me, just re-read your post and it does make sense, yet in some weird way I don't get it, although the maths makes sense. It is one of those weird things that doesn't appear to make sense unless looked at differently.
   
   Thanks

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4. 60

   paradigmsearchposted 13 years ago

   And this statement is an error:
   
   "£27 paid by the friends for their meal + £2 tip for the waiter = £29."
   
   The correct statement would be:
   
   "27 paid by the friends. 25 for the meal + 2 for the waiter = 27."
   
   Or
   
   "27 paid by the friends for their meal and tip for the waiter. 25 for the meal. 2 for the waiter. total 27."

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   1. 89

      mistyhorizon2003posted 13 years agoin reply to this

      I agree, that should read '£25 for the meal and £2 for the waiter'.
      
      Still can't quite get my head around the 'missing' £1 though, (Maths was never my strong point).

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5. 89

   mistyhorizon2003posted 13 years ago

   I think I am starting to get it, but it takes me a while with maths. Once I sleep on it I guess it will be clear to me

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6. 45

   Dale Nelsonposted 13 years ago

   This how the accounting system works for tax.
   
   A bill of 25.00 means each persons bill was for 8.33 which is 1.67 change each from $10 each.
   
   They each kept the dollar. and each gave the 67 cents to the waiter.Have to factor in decimals if you want to be exact.
   
   The 67 x 3 gives the waiter his $2.

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7. 60

   cally2posted 13 years ago

   I used to give this problem to 13 year olds in the classroom. It could keep them puzzling for ages and teacher got an easy day

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8. 60

   Mark Ewbieposted 13 years ago

   This is why I never leave a tip.

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   1. 60

      paradigmsearchposted 13 years agoin reply to this

      

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9. 67

   2uesdayposted 13 years ago

   The moral of the story really is if you are going to worry about the bill then eat at home. 
   
   I am good at adding up figures, but when a bill arrives in a restaurant something about the way they write it out always throws me into confusion.
   
   The other thing I hate is when I am in a bank to get cash and they ask me how I want the money (what notes). I am always worried I will ask for it in notes that do not add up to the amount I have requested. The daft thing is it is only for a small amount of cash for shopping anyway.

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   1. 62

      kephriraposted 13 years agoin reply to this

      I hate in when people ask stupid unneccsary stuff like that .
      - you could ask if you had any particular requirements.
      
      It's like in the supermarket by me they put stuff into bags for you, and sometimes they ask if you want it all in one bag or in two, and I never know what to say - you can't just put on a sarcastic voice and say that it depends whether the first bag gets full or not.

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   2. 61

      readytoescapeposted 13 years agoin reply to this

      Do you have three tens for a twenty?

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10. 61

    readytoescapeposted 13 years ago

    Or
    
    Excuse me, can you break a twenty for four tens?

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11. 89

    mistyhorizon2003posted 13 years ago

    Thanks for all the replies everyone. Honestly, it has kept me up all night thinking about it (I have a headache now).
    
    On the program itself they showed the 3 friends in the restaurant each putting down their £10. They explained that the bill was for £25 and that the waiter brought back the change in £1 coins to be sure they would leave him a tip. They each removed £1, leaving two on the plate.
    Afterwards the host of the show went onto the streets and randomly showed groups of people the scenario, he then asked each of them how much each friend had paid for their meal. Without exception they all deduced that £10 put down, £1 change received = £9 paid for their meal, which sounds logical... that is of course until you multiply the 9 by 3 (the number of friends), and realise that adds up to 27, which sounds like there should have been £3, not £2 left on the waiter's plate. From what I heard no-one could work it out, they were all completely stumped as to how to explain where the 'missing' £1 had gone.
    
    I still find it hard to get my head around, as I can see it easily if I reverse the situation and think of it as each person essentially putting down exactly £9, instead of a £10 note. This would then obviously be £27 in total for the meal, £25 for food and a £2 tip for the waiter = £27 (3 x £9). Maths obvious. So why is it so hard to understand it if they each put down the £10 note?

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    1. 83

       Pcunixposted 13 years agoin reply to this

       Because you are thinking of the original $30 rather than the $27.00 they actually paid.  It's the  three $10 bills that keep making you think that.  The "bearing in mind each person put down £10 initially, totalling £30" locks your mind onto that rather than the $27 given for the $25 bill that you should be focusing on.

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12. 83

    Pcunixposted 13 years ago

    My wife got very mad at me once when she did the math wrong and thought I had left a giant tip to an admittedly cute waitress.  Her math was as confused as this and I actually had to show her with real money that I had only left the 20% she had asked me to..
    
    It wasn't the cute waitress that bothered her - it was the cash!

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13. 76

    Penteposted 13 years ago

    The way you state the puzzle shows where your thinking error is located. You stated that each person paid $9 for the meal for a total of $27. Then an additional $2 for the tip. That way of wording it is incorrect. Each person paid $9 ($10 paid - $1 returned) for (the meal and the tip) combined for a total of $27. That $27 covered the $25 meal and the $2 tip.
    
    Pcunix and I both immediately recognize the problem, because those type of thinking errors would make programming a computer next to impossible.

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    1. 60

       couturepopcafeposted 13 years agoin reply to this

       Pente - you are correct.  I expected pcunix to get it.  This problem is several decades old and originated in an elite university posed by one of their professors.

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    2. 89

       mistyhorizon2003posted 13 years agoin reply to this

       Nooooo, I didn't mean that, what I said was not "each person paid $9 for the meal for a total of $27. Then an additional $2 for the tip.", what I said was  "£25 for food and a £2 tip for the waiter = £27 (3 x £9)".
       
       So glad on this basis I am not a computer programmer
       
       Still a bit confused, reminds me of maths lessons at school.... so far Camlo is winning on making this more clear to me!!

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14. 74

    Aficionadaposted 13 years ago

    The program/documentary used the incorrect wording to turn easy everyday math into a brain teaser. There never was any missing £1.  They just said it that way to make people think.
    
    There are actually three distinct groupings within the £30:  £25 for the dinner; £2 for the tip; £3 for the change back (so that each patron's bill was actually £9, rather than £10). 
    
    The £2 total tip was included in the £27 total (already pointed out immediately above and earlier).  That's where the tricky wording came in.  They tried to make it sound like the £2 was separate from the £27, but it wasn't.  It was the £3 in change that was separate from the £27.
    
    The part that is a real brain teaser to me is:  Why was the tip so low?  Is that normal?  Here in the US, we usually think of a restaurant tip of 15-20%, which would have been £3.75-£5. A £2 tip for a £25 meal is only 8%!

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    1. 83

       Pcunixposted 13 years agoin reply to this

       Good point.  I would have just left the $30.00.

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       1. 80

          camloposted 13 years agoin reply to this

          Me too.

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       2. 89

          mistyhorizon2003posted 13 years agoin reply to this

          I wish they had LOL

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       3. 60

          Pierre Savoieposted 13 years agoin reply to this

          Yes, abandon that  £30, or $30, whatever; it is CURSED.  The way it divides and shimmers will drive you MAD!

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15. 80

    camloposted 13 years ago

    Hi Cindy!
    I looked at it like this: Each paid 8.33 (25.00 divided by 3), plus 1.00 tip, which makes 9.33. 3 x 9.33 makes 28.00, plus 2.00 for the waiter which makes 30.00.

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    1. 89

       mistyhorizon2003posted 13 years agoin reply to this

       Hi Camlo, funnily enough, driving into town to pick up my Husband from work tonight, this train of thought began to occur to me. You have worded it in a way that kind of echoes how I was beginning to think. Thanks for this (and to everyone else for trying to find words that make it clearer to understand). Really, I am not thick, but this is a brain teaser, and although I have done lots of bookkeeping in my time, this one just threw me completely.

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       1. 83

          Pcunixposted 13 years agoin reply to this

          As i said, it is worded to lead your mind in the direction of error.
          
          Don't be hard on yourself - it was cleverly done.

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          1. 89

             mistyhorizon2003posted 13 years agoin reply to this

             Thanks Pcunix, I feel better already, (and my brain aches less)

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16. 53

    MindFlex Home Tuitionposted 4 years ago

    Hey mistyhorizon2003, you should think about hiring a tutor to help you with your Math problem. They also have online lessons, so you will be able to get the help you need from your home.
    
    Visit singaporetuitionteachers.com for more information.

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