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Algebra problem solving task

  1. Aug 23, 2014 #1
    Am a little stuck on a question in my maths homework. Here goes. $6570 to be divided among members of a family. 9 other members of the family find out about the cash and insist on there share. as a result the share was reduced by $120.

    Find original number of family members.

    So far ive got.
    S=Individual share of money
    X=Original number of family members

    S-120= $6570/x+9
    (x+9)(S-120)=6570
    XS-x120+S9-1080=6570
    XS-x120+S9=7650

    Am not sure if im on the right track or not and im not sure where to go from here. Any help appreciated.
     
  2. jcsd
  3. Aug 23, 2014 #2

    ehild

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    Use parentheses. It has to be written $6570/(x+9)

    It is the right track, but you can write S in terms of x. If $6570 is divided among x people, what is the share of one person?

    ehild
     
  4. Aug 23, 2014 #3
    What do you mean by write S in terms of X?
     
  5. Aug 23, 2014 #4

    ehild

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    S is the original share, 6570 divided by among people. How do you write it mathematically?

    ehild
     
  6. Aug 23, 2014 #5
    Should i divide both sides by XS? I know i need to isolate one of the terms. Just not sure how to go about it.
     
  7. Aug 23, 2014 #6

    ehild

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    No. Answer my question. What is the amount one person gets if 6570 is divided among x people?

    Say, there are 10 people in the family, so x=10. How much one person gets?

    ehild
     
  8. Aug 23, 2014 #7
    6570/x+9 6570/19 = 324.73
     
  9. Aug 23, 2014 #8

    ehild

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    No, I meant the original amount, they got before the other family members arrived.

    You share 24 apples among 4 people, how many apples does on person get? If two more persons come and they also want their share, hove many it will be?

    And I do not understand what you wanted to say. You wrote that 6570 is divided by x and 96570 divided by 19 and the ratios added. Where did you get that 96570 from????? If x=10, that sum is 5740 instead of 324.73.


    ehild
     
  10. Aug 23, 2014 #9

    Ray Vickson

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    Wrong.
    [tex] \frac{6570}{x} + 9 \neq 324.73[/tex]
    If you mean
    [tex] \frac{6570}{x+9}[/tex]
    then take the trouble to write it properly, using parentheses, like this: 6570/(x+9). It is not hard to do, and makes everything much more readable.
     
  11. Aug 23, 2014 #10

    Mark44

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    To the OP,
    6570/x + 9 means ##\frac{6570}{x} + 9##, which is not what you intended. As Ray says, use parentheses to write what you mean.

    Also, what you wrote in the earlier post is missing an equals sign, leading to additional confusion.
    This should be 6570/(x + 9) = 6570/19 = <whatever>
     
  12. Aug 23, 2014 #11
    Am really sorry ill keep all that in mind. I seriously have no idea where to go with this. Ive tried the method of elimination/substitution. Does this perhaps have to be a quadratic function?
     
  13. Aug 24, 2014 #12

    ehild

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    You will get a quadratic equation for x.

    ehild
     
  14. Aug 24, 2014 #13
    Hey I ended up working it out. Took me a good few hours but yes I ended up with a quadratic. Thanks for the help. :)
     
  15. Aug 24, 2014 #14

    ehild

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    I am pleased. What did you get for x?

    ehild
     
  16. Aug 25, 2014 #15
    For the purpose of this thread I did change the equation a bit from the my homework as a result I got decimal numbers which may seem a bit strange.

    S I got 250.28 and X i got 26.25
     
  17. Aug 25, 2014 #16
    You have x people initially, and each one of them was to get S dollars. How many dollars does this amount to in total (in terms of x and S only)? How is this related to the $6570?

    Chet
     
  18. Aug 25, 2014 #17
    What is the original statement of the problem that gives you these numbers? If X represents a number of family members, does a fractional number for family members make sense?
     
  19. Aug 25, 2014 #18

    SteamKing

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    You should check your calculations by using your value of x in the original problem statement.
    I worked through the algebra and I got a different result.

    You also can't have a fraction of a person showing up to claim a share, since the number of humans is maddeningly restricted to the set of positive integers.
     
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