Question 130559
One number is twice another:  {{{x=2y}}}
The sum of their reciprocals is {{{3/28}}}:  {{{(1/x)+(1/y)=3/28}}}


Step 1, substitute:
{{{cartoon((1/red(x))+(1/y)=3/28,(1/red(2y))+(1/y)=3/28)}}}


Step 2, apply common denominator:
{{{cartoon((1/2y)+red((2/2))(1/y)=3/28,(1/2y)+red((2/2y))=3/28)}}}


Step 3, add the fractions:
{{{cartoon(red((1+2))/2y=3/28,red(3)/2y=3/28)}}}


Step 4, since the numerators of these two equal fractions are equal, the denominators must also be equal:
{{{cartoon(red(3)/2y=red(3)/28,2y=28)}}}


Step 5, solve:
{{{cartoon(2y/red(2) = 28/red(2),y=14)}}}


Step 6, substitute derived value for y into {{{x=2y}}}
{{{cartoon(x=red(2y),x=red(2*14),x=red(28))}}}


Check your answer:
{{{28 = 2* 14}}}
{{{cartoon(1/28+red(1/14)=3/28,1/28+red(2/28)=3/28)}}}  Answer checks.