Question 1153238


let a number be {{{x}}} 

{{{1/5 }}}of that number is {{{x/5}}} 

{{{1/6}}} of that number is {{{x/6}}} 

if they are added, we have {{{x/5+x/6}}}

if the result is {{{82}}}, we have {{{x/5+x/6=82}}}

to find the original number, solve 

{{{x/5+x/6=82}}}

{{{6x/(6*5)+5x/(5*6)=82}}}

{{{6x/30+5x/30=82}}}.....both sides multiply by {{{30}}}

{{{30(6x/30)+30(5x/30)=82*30}}}

{{{6x+5x=2460}}}

{{{11x=2460}}}

{{{x=2460/11}}}=> exact solution


check:

{{{x/5+x/6=82}}}

{{{(2460/11)/5+(2460/11)/6=82}}}

{{{2460/55+2460/66=82}}}

{{{44.72727272727272+37.27272727272727=82}}}

{{{82=82}}}