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Math Help - Using averges to find the total

  1. #1
    Member GAdams's Avatar
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    Using averges to find the total

    Jane and Mitzi have both done the same number of practice papers for their mathematics examination.
    They both have the same total mark, T.
    They do one more practice paper.
    Jane scores 89 and her average score increses to 68.
    Mitzi scores 57 and her average score decreases to 64.

    Find the final number of practice papers taken by each student.

    -How would I work this one out, thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by GAdams View Post
    Jane and Mitzi have both done the same number of practice papers for their mathematics examination.
    They both have the same total mark, T.
    They do one more practice paper.
    Jane scores 89 and her average score increses to 68.
    Mitzi scores 57 and her average score decreases to 64.

    Find the final number of practice papers taken by each student.

    -How would I work this one out, thanks.
    Let the number of papers be N.

    After the extra paper we have for Jane:

    68 = (T + 89)/(N+1)

    and for Mitzi:

    64 = (T+ 57)/(N+1)

    or rearranging:

    68N - T = 21
    64N - T = -7

    which you may solve to find that N = 7.

    RonL
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  3. #3
    Member GAdams's Avatar
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    Jane
    68N + 68 = T + 89

    68N + 68 - 89 = T

    68N - 21 = T

    Substituted this into second equation:

    64N + 64 = T + 57

    64N + 64 = 68N - 21 + 57

    64N - 68N = -21 + 57 - 64

    -4N = -28

    N = -28/4

    N = -7

    Wrong? Also, the answer in the practice paper is 8.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by GAdams View Post
    Jane
    68N + 68 = T + 89

    68N + 68 - 89 = T

    68N - 21 = T

    Substituted this into second equation:

    64N + 64 = T + 57

    64N + 64 = 68N - 21 + 57

    64N - 68N = -21 + 57 - 64

    -4N = -28

    N = -28/4

    N = -7

    Wrong? Also, the answer in the practice paper is 8.
    I solved for N, which is the number of papers before the extra one.
    I should have made that clearer.

    RonL
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by GAdams View Post
    Jane
    68N + 68 = T + 89

    68N + 68 - 89 = T

    68N - 21 = T

    Substituted this into second equation:

    64N + 64 = T + 57

    64N + 64 = 68N - 21 + 57

    64N - 68N = -21 + 57 - 64

    -4N = -28

    N = -28/4
    No, -4N = -28, so 4N = 28, or N=7.

    N = -7

    Wrong? Also, the answer in the practice paper is 8.
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  6. #6
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    Hello, GAdams!

    Let's start this again . . .


    Jane and Mitzi have both done the same number of practice papers.
    They both have the same total mark, T.
    They do one more practice paper.
    Jane scores 89 and her average score increases to 68.
    Mitzi scores 57 and her average score decreases to 64.

    Find the final number of practice papers taken by each student.

    Let N = final number of practice papers.

    Jane has a total of T points and scores 89 more.
    Her average is 68: .(T + 89)/N .= .68 . . . . 68N - T .= .89 .[1]

    Mitzi has a total of T points and scores 57 more.
    Her average is 57: .(T + 57)/N .= .64 . . . . 64N - T .= .57 .[2]

    Subtract [2] from [1]: . 4N = 32 . . . . N = 8

    Therefore, they each took 8 practice papers.

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