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Math Help - Worded algebra problem.

  1. #1
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    Worded algebra problem.

    Dear sir ,
    I would appreciate if anyone can show me the solution to the below question.
    thanks
    Kingman

    Jane and John wish to buy a book. However, Jane needs seven more cents to buy the book, while John needs one more cent. They decide to buy only one book together but discover that they do not have enough money. What is the price of the book?
    Last edited by mr fantastic; March 14th 2011 at 06:31 PM. Reason: Re-titled.
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  2. #2
    Senior Member Sambit's Avatar
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    Suppose Jane has 'x' cents and John has 'y' cents. Then first tell me, what can you say about the price of the book in terms of 'x' and 'y'?
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  3. #3
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    That is exactly my problem.
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  4. #4
    Senior Member Sambit's Avatar
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    Jane needs 7 cents MORE so the price of the book is x+7. Again, John need 1 cent MORE, so the price of the book is y+1. Can you verify it now, by looking at the problem?


    Suppose you have 10 cents in your hand, and you need 5 more cents to buy the book. What is the price of the book then?
    Last edited by Sambit; March 14th 2011 at 04:41 AM. Reason: info added
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  5. #5
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    You said ", Jane needs seven more cents to buy the book". What is 7 more than x?

    "John needs one more cent". What is 1 more than y?

    But I don't think you need to set up equations. When John and Jane put their money together, they still do not have enough money. Yet, John needed only one cent more. What does that tell you about how much money Jane had? And, therefore, what was the price of the book?

    (These are not very realistic numbers!)
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  6. #6
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    The hint given is: One should know that books in this shop are very cheap! I do not know how use this given information
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  7. #7
    Senior Member Sambit's Avatar
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    See what HallsofIvy said. If the price is M, then x+y\leq M and y+1=M which basically means x+M-1\leq M ie x\leq 1!!! Funny thing! Further manipulation gives M=7 to some value less than 8!
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by kingman View Post
    Jane and John wish to buy a book. However, Jane needs seven more cents to buy the book, while John needs one more cent. They decide to buy only one book together but discover that they do not have enough money. What is the price of the book?
    I don't get this one myself. If they are only going to buy one book between them, then why doesn't John get 1 penny from Jane? The only way this can't be done is if Jane has no money at all. So since Jane has no money and she needs 7 more cents to buy one that means the book costs 7 cents. But this solution seems kind of ridiculous as the problem statement implies that Jane does actually have some money...

    -Dan
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  9. #9
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    Quote Originally Posted by topsquark View Post
    I don't get this one myself. If they are only going to buy one book between them, then why doesn't John get 1 penny from Jane? The only way this can't be done is if Jane has no money at all. So since Jane has no money and she needs 7 more cents to buy one that means the book costs 7 cents. But this solution seems kind of ridiculous as the problem statement implies that Jane does actually have some money...

    -Dan
    Book =x
    John =x-1
    Jane =x-7

    x-1+x-7=x
    2x-8=x
    x=8

    Jane = 1
    John = 7

    But it doesn't seem right, because if they put their money together, they can buy the book.

    Only way I see it is that if Jane has 0 cent.
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  10. #10
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    Quote Originally Posted by ikislav View Post
    Book =x
    John =x-1
    Jane =x-7

    x-1+x-7=x
    This is incorrect. This would be the case if they, together, had enough money to buy the book. We were told that they do NOT have enough money, together, to buy the book.
    What you can say is that (x-1)+ (x- 7)< x

    2x-8=x
    x=8

    Jane = 1
    John = 7

    But it doesn't seem right, because if they put their money together, they can buy the book.

    Only way I see it is that if Jane has 0 cent.
    Exactly! If John needed only one more cent to buy the book- and Jack and Jane together did not have enough money to buy it, then Jane has no money. That means that John has 6 cents and the book cost 7 cents.

    (This is assuming integer pennies. If we allow "ha'pennies" then Jane could have one halfpenny so the book cost 6 and 1/2 pennies and John has 5 and a half pennies.)
    Last edited by HallsofIvy; March 15th 2011 at 12:17 PM.
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  11. #11
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    Quote Originally Posted by HallsofIvy View Post
    This is incorrect. This would be the case if they, together, had enough money to buy the book. We were told that they do NOT have enough money, together, to buy the book.
    What you can say is that (x-1)+ (x- 7)< x
    Yes, thank you for correcting that.
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