<s>[INST] How to get the man's age. I am very much in need of solution for this problem. I can't figure out the answer for this. does anybody know about this problem below? 
thanks,,
Problem:
A man's boyhood lasted for 1/6 of his life, he played soccer for the next 1/12 of his life, and he married after 1/7 more of his life. a daughter was born 5 years after his marriage & the daughter lived 1/2 as many years as her father did. If the man died four years after his daughter did, how old was the man when he died? 
 [/INST] We can set up this problem by adding all the fractions of his life so they equal $1$ (his whole life). Also, let's say that he lived to $x$ years old.
Now,
$\frac{1}{6}$ of his life was boyhood.
$\frac{1}{12}$ of his life was soccer.
$\frac{1}{7}$ of his life was end of soccer to marriage.
After $5$ years, his daughter was born so
$\frac{5}{x}$ of his life was marriage to daughter's birth.
His daughter lived half the amount of years that he will have lived so
$\frac{1}{2}$ of his life was his daughter's life.
Then he died $4$ years later so
$\frac{4}{x}$ of his life was from his daughter's death to his death.
And all of these should equal to $1$. Thus
$\frac{1}{6}+\frac{1}{12}+\frac{1}{7}+\frac{5}{x}+\frac{1}{2}+\frac{4}{x}=1$
Now we simply solve for $x$. We get
$\frac{9}{x}=1-\frac{1}{6}-\frac{1}{12}-\frac{1}{7}-\frac{1}{2}$
then $9=x(1-\frac{1}{6}-\frac{1}{12}-\frac{1}{7}-\frac{1}{2})$
then $x=\frac{9}{1-\frac{1}{6}-\frac{1}{12}-\frac{1}{7}-\frac{1}{2}}$.
By simplifying, we get $x=84$. So he lived to $84$ years old.
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