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math 1

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The average of 10 numbers is 12. If one number is removed, the average is 11. What number is removed?

  • math 1 -

    ( a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10 ) / 10 = 12 Multiply both sides by 10

    a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10 = 120


    ( a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 ) / 9 = 11 Multiply both sides by 9

    a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 = 99


    ( a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 ) + a10 = 120

    99 + a10 = 120 Subtract 99 to both sides

    99 + a10 - 99 = 120 -99

    a10 = 21


    Number 21 is removed.

  • math 1 -

    the total of the 10 number is 120

    solve

    (120-x)/9 = 11
    120-x = 99
    -x = -21
    x = 21

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