# Re: Amount of Money

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Posted by Brad Paul on November 01, 2002 at 13:05:36:

In Reply to: Amount of Money posted by Randy on November 01, 2002 at 12:06:23:

: \$40,000 was won in a lottery. After taxes of 25 per cent, the money was divided as follows: the mother received twice as much as the three sons, the two sisters received 500 dollars in addition to 1/5 as much as the mother. How much did each receive?

If I known how much one of the three sons got this problem would be very easy.

So I will pretend I do know, but I'll call it x. Also because I do not
like numbers I'm going to let the tax rate be t(=.25), the lotto-pot
be w(=40000) (for winnings) and the 500 extra dollars be e.

Each son got x dollars.

Mom got: 2(x+x+x) =6x This is twice as much at the three sons.

(Here is an interpretation of the question issue. Did mom get twice as
much as the sum of the three sons or twice as much as one of the three
sons? I'm going to assume the first case. If I'm wrong mom would get
just 2 x Then you can use this term to solve the problem)

The each of the two sisters got: 6x/5+e

What is the sum of everyone's money?

3x+6x+2(6x/5+e)

3x for the three sons

6x for mom

2(6x/5+e) for the two sisters

Set this equal to the lotto-pot after taxes.

w(1-t)=3x+6x+2(6x/5+e)

Solve for x

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