Question 1152980

let larger part  be {{{x}}} and  smaller part {{{y}}}


{{{x+y=15}}}
{{{x=15-y}}}.........eq.1

when the larger is divided by {{{3}}} and the smaller is divided by {{{2 }}} the quotients are equal:

{{{x/3=y/2}}}.......solve for {{{x}}}

{{{x=3y/2}}}.......eq.2

from eq.1 and eq.2 we have

{{{15-y=3y/2}}}........solve for {{{y}}}

{{{30-2y=3y}}}

{{{30=3y+2y}}}

{{{5y=30}}}

{{{y=6}}}

then

{{{x=15-y}}}.........eq.1
{{{x=15-6}}}
{{{x=9}}}

 two parts are {{{9}}} and {{{6}}}