1. ## maths problem

I HAVE NO IDEA HOW TO DELETE A DOUBLE POST

SORRY

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?

2. 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 $\displaystyle 1+\frac{1}{7}(x-1)=\frac{x+6}{7}$ dollars.

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

As these are equal, equate and solve for x:

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

$\displaystyle x=36$

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 $\displaystyle \frac{36}{6}=6$ 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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