<PRE><B>Question 97184</B>
The smaller of two numbers is two-thirds of the larger,
One number = x;  smaller number = {{{(2x)/3}}}
:
the sum of their reciprocals is 1/6. 

{{{1/x}}} + {{{3/(2x)}}} = {{{1/6}}}
:
What are the numbers?
:
The common denominator would be 6x, multiply equation by 6x
6x*{{{1/x}}} + 6x*{{{3/(2x)}}} = 6x*{{{1/6}}}
:
Cancel the denominators leaving:
6(1) + 3(3) = x(1)
6 + 9 = x
x = 15 is one number
:
The smaller:
{{{2/3}}}*15 = 10
:
:
Check solution in original equation:
{{{1/15}}} + {{{1/10)}}} = {{{1/6}}}
{{{2/30}}} + {{{3/30)}}} = {{{5/30}}}</PRE>