Question 942174


the ratio of bobs cards {{{x}}} to gregs cards {{{y}}} was {{{3:4}}}

{{{x:y=3:4}}}............eq.1

after bob bought {{{12}}} cards and greg lost {{{24}}} cards the
ratio became {{{3:2}}} 

{{{(x+12):(y-24)=3:2}}}............eq.2

{{{x:y=3:4}}}............eq.1

{{{4x=3y}}}

{{{y=4x/3}}}



{{{(x+12):(y-24)=3:2}}}............eq.2

{{{2(x+12)=3(y-24)}}}

{{{2x+24=3y-72}}}..........plug in {{{y=4x/3}}}


{{{2x+24=3(4x/3)-72}}}

{{{2x+24=4x-72}}} ......solve for {{{x}}}

{{{72+24=4x-2x}}}

{{{96=2x}}}

{{{x=48}}}

and {{{y=4x/3}}} => {{{y=(4*48)/3}}} => {{{y=64}}}

 the total number of cards Bob  had at first {{{48}}}

and Greg  had at first {{{64}}}