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Math Help - Where is the missing number?

  1. #1
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    Where is the missing number?

    Can anyone help me answer this?..

    You see a shirt for 97, but you don't have any money.
    You borrow 50 from your mum, and 50 from your dad, so you have 100.
    You buy the shirt, and have 3 change.
    So you give your mum 1, your dad 1 and keep the other 1.
    You now owe your mum 49 and your dad 49.
    49 + 49 = 98 and your 1 makes 99.


    Where is the missing 1?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Where is the missing number?

    Quote Originally Posted by benjiman46 View Post
    Where is the missing 1?
    You owe 49 pounds to your dad and 49 to your mum. You have 1 pound so, you need another pound to payng your debt.
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  3. #3
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    Re: Where is the missing number?

    Think of it this way:
    Your debt is 100 pounds combined. After giving back 1 pound to your mom and 1 pound to 1 dad reduces your debt by 2. So now your debt is 98 pounds. That means that any number of pounds you have with you can only be used to reduce the debt, and not to increase it. In terms of mathematical operations, the number of pounds you have with you can only be subtracted from the total debt, not added to the debt. The one pound you are left with can only be used to reduce your debt by one, meaning it cannot be added to 98 to get the result 99, but only subtracted from 98 to get the correct answer 97. Get it?

    Nothing is missing, you are just forced into paradox by the incorrect operation performed between the debt of 98 pounds and the one pound you have with you.

    I hope nothing is lost in translation since English is not my native language.
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  4. #4
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    Re: Where is the missing number?

    Quote Originally Posted by FernandoRevilla View Post
    You owe 49 pounds to your dad and 49 to your mum. You have 1 pound so, you need another pound to payng your debt.
    Oh professor, you should know better than that!
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  5. #5
    MHF Contributor FernandoRevilla's Avatar
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    Re: Where is the missing number?

    Quote Originally Posted by MathoMan View Post
    Oh professor, you should know better than that!
    I didn't explain it well. Your correct approach is about the coherence of the shirt's price, and mine one about the coherence of the debt. In your case 49+49-1=97, in my case 100=1+1+(98-1)+1(\mbox{the pound the son has}).
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  6. #6
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    Re: Where is the missing number?

    No hard feelings professor, I was just teasing you a bit. Math on!
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  7. #7
    MHF Contributor FernandoRevilla's Avatar
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    Re: Where is the missing number?

    Quote Originally Posted by MathoMan View Post
    No hard feelings professor, I was just teasing you a bit. Math on!
    No problem, I am very fond of irony (although provisionally retired, I must confess).
    Last edited by FernandoRevilla; April 14th 2012 at 01:35 AM.
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  8. #8
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    Re: Where is the missing number?

    Solution: anyone who pays 97 for a single shirt is obviously crazy. Therefore the "missing 1" is the result of a psychotic episode!
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  9. #9
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    Re: Where is the missing number?

    Quote Originally Posted by HallsofIvy View Post
    Solution: anyone who pays 97 for a single shirt is obviously crazy. Therefore the "missing 1" is the result of a psychotic episode!
    Yep, but that solution is the trivial one.
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