Question 269710
Let {{{x}}} = number of years the man was alive
boyhood = {{{(1/6)*x}}}
years played football = {{{(1/8)*x}}}
years between football and marriage = {{{5}}}
years after marriage daughter was born = {{{(1/12)*x}}}
years Daughter was alive = {{{(1/2)*x}}}
years after daughter died that man died = {{{6}}}
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All of this added together is the man's whole lifetime, so
{{{x = (1/6)*x + (1/8)*x + 5 + (1/12)*x + (1/2)*x + 6}}}
Multiply both sides of equation by {{{24}}}
{{{24x = 4x + 3x + 120 + 2x + 12x + 144}}}
{{{24x - 4x - 3x - 2x - 12x = 264}}}
{{{24x - 21x = 264}}}
{{{3x = 264}}}
{{{x = 88}}}
The man lived to be 88 years old
check:
{{{x = (1/6)*x + (1/8)*x + 5 + (1/12)*x + (1/2)*x + 6}}}
{{{88 = (1/6)*88 + (1/8)*88 + 5 + (1/12)*88 + (1/2)*88 + 6}}}
{{{88 = 88*(1/6 + 1/8 + 1/12 + 1/2) + 11}}}
{{{Divide both sides by {{{88}}}
{{{1 = 1/6 + 1/8 + 1/12 + 1/2 + 11/88}}}
{{{1 = 4/24 + 3/24 + 2/24 + 12/24 + 3/24}}}
{{{1 = 24/24}}}
OK