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Linear equations algebra based problem

  1. Apr 7, 2016 #1
    1. The problem statement, all variables and given/known data
    I got following Question from a book:

    I am doing it using a different method but my answer is wrong. Can somebody please guide me, what is the problem with it??
    The question is:


    In 1999, Diana read 10 English books and 7 French books. In 2000, she read twice as many French books as English books. If 60% of the books that she read during the two years were French, how many books did she read in 2000?

    2. Relevant equations
    Linear equation in single variable based problem

    3. The attempt at a solution
    1999: E(10), F(7) = 17

    2000: E(x), F(2x)

    Two years total books = 10 + 7 + x + 2x

    1.666x /*60 % */ + 2.5x /* 40 */ = 17 + 3x

    4.166 - 3x = 17

    X = 14.579

    2x = 29

    Total = 15 + 29 = 44 (wrong answer)

    Some body please guide me.

    Zulfi.
     
  2. jcsd
  3. Apr 7, 2016 #2
    are you applying this condition correctly?
    as the snag must lie here.
     
  4. Apr 7, 2016 #3

    SteamKing

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    So far, so good.

    3x is the total number of books read in 2000 (3x = 2x [French] + x [English])

    17 + 3x = total number of books read in 1999 and 2000.

    How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?
     
  5. Apr 7, 2016 #4
    Hi,
    Thanks for your reply.
    <How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?>

    I am trying to work in a different way:

    According to the question, it says:
    <If 60% of the books that she read during the two years were French>
    60% is French so 40% should be english.
    60% = 1.666
    & 40% = 2.5
    So 1.666x + 2.5x = 17 + 3x
    I want to do it in this way. Please tell me what's wrong with it?

    Zulfi.
     
  6. Apr 7, 2016 #5
    ?? what does the above statement means?
     
  7. Apr 7, 2016 #6

    Ray Vickson

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    60% = 60/100, but you wrote 1.666 = 166.6/100!

    If E = number of English books read in year 2000, then the total number of English books read in the two years is N_Eng = 10+E and the total number of French books read in the two years is N_Fr = 7+2E. Now 60% of the total is (6/10)(17 + 3E), and this is supposed to equal the number of French books read. Avoid decimals as long as possible; just work with exact fractions, except maybe at the last minute.
     
  8. Apr 7, 2016 #7

    SteamKing

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    You can do it your way or you can do it the right way -- yer cherce.

    Don't expect your way to get you the correct answer, however.
     
  9. Apr 7, 2016 #8
    Hi,
    <60% = 1.666>
    if you divide any number by 1,666 you would get 60% of that value. For instance if you divide like 200/1.66 you would get 120.48 which is approximately 60% of 200, & you can also write it:
    120/200 * 100 ,
    Similarly if you divide any number by 2.5 you would get 40% of that value.

    If you want me to avoid decimal, i can write it:
    60/100 x + 40/100 x = 17 + 3x
    but x = 27
    & 2x = 54
    so total = 81 (not correct)
    please tell me what's wrong with my solution.

    <How do you express 60% of the total number of books read and then set this quantity equal to the number of French book read in 2 years?>
    Instead of 60% i am considering 100% (i.e 60% French & 40% english) & making it equal to the total books read in 2 years. Why is this approach not possible?

    Zulfi.
     
    Last edited: Apr 7, 2016
  10. Apr 7, 2016 #9

    Ray Vickson

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    Your statement "if you divide any number by 1,666 you would get 60% of that value." is not true; but it is approximately true. Dividing by 1.6666666666666666666666666 would get you closer to a true statement, but no finite number of decimal places will give you an exact statement like the one you want. Of course, I know perfectly well that using 3 or 4 decimal places is often good enough in practice, but the point I am making is that you said something that is only approximately true, and I am not sure you actually realize that.
     
  11. Apr 7, 2016 #10

    SteamKing

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    I'm frankly puzzled why anyone would want to divide to find 60% of something when this proportion can be as easily determined by multiplying the whole by 0.6.
     
  12. Apr 7, 2016 #11

    Mark44

    Staff: Mentor

    Don't write stuff like this -- neither one makes any sense.
    60% of what equals 5/3?
    40% of what equals 5/2?
    There needs to be a variable in place of each what.
     
  13. Apr 8, 2016 #12
    Hi,
    Okay, 0.6 is also logical, so for question in this thread I have for the combine 2 years books read by her are:
    0.6 + 0.4 = 17 + 3x but now i am getting the answer in minus.
    Whats getting wrong when i am considering the whole 100%. There are only two books, if composition of french is 60% then composition of English should be 40% but why its not working.
    Some body please tell me my mistake.
    Zulfi.
     
  14. Apr 8, 2016 #13

    SteamKing

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    Your mistake is that 0.6 + 0.4 = 17 + 3x is not the correct equation to use here.

    To recapitulate the problem statement:
    First of all, forget the 0.40. That doesn't come into consideration at all.

    Figure out how many French books Diana read in 1999 and 2000, using what information is given in the statement above.

    You are told she read 7 French books in 1999, and 10 English books. How many books did Diana read in 1999?

    In 2000, Diana read twice as many French books as English books. Since the number of English books or French books read is unknown, you would pick one kind of book and say that Diana read x of them in 2000.

    So, the next step here is to express the number of books which Diana read in 2000.

    Write an expression for the total number of books Diana read in 1999 and 2000.

    60% of this total number of books read is equal to the number of French books Diana read in 1999 and 2000. How would you express this?

    Solve this last expression for x, and then calculate the number of books Diana read in 2000.
     
  15. Apr 9, 2016 #14
    Hi,
    Thanks for your reply & i appreciate all of you for helping me. Its a great forum & i am getting help immediately.
    However if you are saying this:
    <First of all, forget the 0.40. That doesn't come into consideration at all.>
    Then it means the end of this thread. Because my interest in this question was particularly due to 40%. Otherwise the solution is mentioned in the book.
    Any how I tried different options & it turns out that you people are right.

    Zulfi.
     
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