Question 1175686

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


{{{b/g=3/4}}}
{{{b=3g/4}}}.....eq.1

{{{(b+6)/(g-6)=4/3}}}
{{{b+6=4(g-6)/3}}}
{{{b+6=(4g-24)/3}}}
{{{b+6=4g/3-8}}}
{{{b=4g/3-8-6}}}
{{{b=4g/3-14}}}.....eq.2

from eq.1 and eq.2 we have

{{{3g/4=4g/3-14}}}
{{{14=4g/3-3g/4}}}
{{{14=16g/12-9g/12}}}
{{{14=7g/12}}}
{{{7g=14*12}}}
{{{g=14*12/7}}}
{{{g=2*12}}}
{{{g=24}}}

go to

{{{b=3g/4}}}.....eq.1, substitute {{{g}}}

{{{b=(3*24)/4}}}
{{{b=3*6} }}
{{{b=18}}}


so, {{{24}}}girls were originally in the group