Question 669185
Write an equation for each statement; the two numbers are a & B
:
 the sum of the reciprocals of two number is 5/8.
{{{1/a}}} + {{{1/b}}} = {{{5/8}}}


 four times the reciprocal of the first is twice as much as eight times the reciprocal of the second.
{{{4(1/a)}}} = {{{2(8/b)}}}
which is
{{{4/a}}} = {{{16/b}}}
cross multiply
4b = 16a
divide both sides by 4
b = 4a
:
find the numbers.
Back to the 1st equation, replace b with 4a
{{{1/a}}} + {{{1/(4a)}}} = {{{5/8}}}
multiply by 8a, results:
8 + 2 = 5a
10 = 5a
a = 2
then
b = 4*2
b = 8
:
:
See if that checks out
{{{1/2}}} + {{{1/8}}} = {{{5/8}}}
{{{4/8}}} + {{{1/8}}} = {{{5/8}}}