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Math Help - help me please

  1. #1
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    help me please

    The average of one group of numbers is 4. A second group contains twice as many numbers and has an average of 10. The average of both numbers combined is.

    a. 5
    b. 6
    c. 7
    d. 6
    e. 9
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  2. #2
    Super Member

    Joined
    May 2006
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    Lexington, MA (USA)
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    Hello, Abigail!

    The average of one group of numbers is 4.
    A second group contains twice as many numbers and has an average of 10.
    The average of both groups combined is:
    . . (a) 5. . (b) 6. . (c) 7. . (d) 8. . (e) 9

    The first group has n numbers and a total of T1.
    . . Hence: .(T1)/n .= .4 . . T1 = 4n .[1]

    The second group has 2n numbers and a total of T2.
    . . Hence: .(T2)/2n) .= .10 . . T2 .= .20n .[2]

    Add [1] and [2]: .T1 + T2 .= .4n + 20n .= .24n


    The total of both groups is: 24n

    There are: .n + 2n .= .3n numbers in the two groups.

    Therefore, the average of both groups is: .24n/3n .= .8 . . . answer choice (d)

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