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Math Help - maths problem

  1. #1
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    Exclamation maths problem

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    this is a famous problem, but i forgot who made it up

    there was a rich man, writing his will. he didnt have any children yet, but wanted each child to have the following:

    first son: 1 gold coin+ 1/7 of all wealth left
    second son: 2 gold coins + 1/7 of whats left after 1st son took
    third son: 3 gold coins + 1/7 of whats left after 2nd son took
    and so on

    how many sons did he have? and how much money did he have?
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  2. #2
    Senior Member DivideBy0's Avatar
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    I assume you want the sons to have equal amounts of money, then the solution is easier than you might think.

    Let x = the value of the father's will, then

    The first son receives 1+\frac{1}{7}(x-1)=\frac{x+6}{7} dollars.

    The second son receives 2+\frac{1}{7}\left(x-\left(\frac{x+6}{7}\right)-2\right)=\frac{6x+78}{49} dollars.

    As these are equal, equate and solve for x:

    \frac{x+6}{7}=\frac{6x+78}{49}

    x=36

    Now it's easy to find the number of sons. Since now we know the first son receives 6 dollars, and all the sons receive the same amount, the man has \frac{36}{6}=6 sons.

    I can't believe how long I spend looking at functions of functions and trying to turn everything into massive overcomplicated expressions, all the while overlooking this easy solution.
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