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Math Help - A father's will

  1. #1
    Senior Member DivideBy0's Avatar
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    A father's will

    A father in his will left all his money to his children in the following manner:

    $1000 to the first born and 1/10 of what then remains,
    then $2000 to the second born and 1/10 of what remains,
    then $3000 to the third born and 1/10 of what then remains, and so on.

    When this was done each child had the same amount. How many children were there?

    Which way is fastest and easiest? :/
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by DivideBy0 View Post
    A father in his will left all his money to his children in the following manner:

    $1000 to the first born and 1/10 of what then remains,
    then $2000 to the second born and 1/10 of what remains,
    then $3000 to the third born and 1/10 of what then remains, and so on.

    When this was done each child had the same amount. How many children were there?

    Which way is fastest and easiest? :/
    Hi,

    I don't know if my way is the easiest. I only did some plausible considerations and a final trial and error - and had success:

    let x be the total amount of money
    let n be the number of children

    Then every child gets x/n

    The first one gets:
    $1000 + 1/10*(x -$1000) = x/n
    $900 + 1/10*x = x/n
    $900 = x*(1/n - 1/10)

    x = $900 / (1/n - 1/10)

    And now starts the guessing: The denominator cann't be negative that means the greatest number for n could be 9. So I took n = 9. That means x = $81,000. Now I checked the money each child will get:
    Code:
    child     gets            remains
    ------------------------------------
      1    $1000 + $8000      $72,000
      2    $2000 + $7000      $63,000
      3    $3000 + $6000      $54,000
      4    $4000 + $5000      $45,000
      :
      :
    So every child gets the same amount of money

    EB
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