Question 1143927

let the number of girls be {{{g}}}, and the number of boys{{{ b}}}

if  there are {{{3}}} more girls than boys, we have
{{{g=b+3}}}..........eq.1

if  the ratio of girls ​to boys is{{{ 6}}} to {{{5}}}, we have

{{{g/b=6/5}}}........eq.2

substitute {{{g}}} from eq.1 

{{{(b+3)/b=6/5}}}........eq.2....solve for {{{b}}}

{{{5(b+3)=6b}}}
{{{5b+15=6b}}}
{{{15=6b-5b}}}
{{{b=15}}}

go to
{{{g=b+3}}}..........eq.1...substitute {{{b}}}
{{{g=51+3}}}
{{{g=18}}}

so, there are {{{18}}} girls  and {{{15}}} boys

check the ratio

{{{18/15=6/5}}}...simplify left side
{{{(18:3)/(15:3)=6/5}}}
{{{6/5=6/5}}}->true