Question 845006


Numbers are {{{x}}} and {{{4x }}}

Sum of reciprocals is

{{{1/x + 1/(4x) = 35/4 }}}................solve for {{{x}}}

{{{4 /4x+ 1/(4x) = 35/4 }}}

{{{5/(4x) = 35/4 }}}

{{{5*4 = 35*4x }}}

{{{5*cross(4) = 35*cross(4)x }}}

{{{5= 35x }}}

{{{x = 5/35 }}}

{{{highlight(x = 1/7)}}} .....first number

{{{4x =4(1/7 )}}}

{{{highlight(4x=4/7)}}}...........second number

their reciprocals:  

reciprocal of {{{1/7}}} is {{{7}}} and reciprocal of {{{4/7}}} is {{{7/4}}}

the sum of reciprocals should be {{{35/4}}} 

check it:

{{{7+7/4=35/4}}}

{{{7*4/4+7/4=35/4}}}

{{{28/4+7/4=35/4}}}

{{{(28+7)/4=35/4}}}

{{{35/4=35/4}}} which confirms our solution is correct