Question 120230
Not counting the charities, he gave away 1/2 plus 1/4 plus 1/5 of his estate.


{{{(1/2)+(1/4)+(1/5)=(10/20)+(5/20)+(4/20)=19/20}}}, which means that he divided 1/20 of his estate among the three charities.  So if his entire estate was valued at x dollars:


{{{3*3400=x/20}}}


{{{20*3*3400=x}}}


{{{x = 204000}}}


Check the answer:

1/2 of $204,000 is $102,000 that went to his wife
1/4 of $204,000 is $51,000 that went to his son
1/5 of $204,000 is $40,800 that went to his niece

$102,000 + $51,000 + $40,800 = $193,800

$204,000 - $193,800 = $10,200

$10,200/3 = $3,400.  Answer checks.


Hope that helps.
John