Question 990125

The ratio of red jelly beans {{{r}}} to yellow jelly beans {{{y}}}  in a dish is {{{3:4}}}. 

{{{r/y=3/4}}}....solve for {{{r}}}
{{{r=3y/4}}}

If Greg eats {{{3}}} red jelly beans and {{{6}}} yellow ones,the ratio is {{{4:5}}}. 

{{{(r-3)/(y-6)=4/5}}}.......substitute {{{3y/4}}} for {{{r}}}

{{{(3y/4-3)/(y-6)=4/5}}}.....cross multiply

{{{5(3y/4-3)=4(y-6)}}}

{{{15y/4-15=4y-24}}}

{{{15y/4-4y=15-24}}}

{{{15y/4-16y/4=15-24}}}

{{{-y/4=-9}}}

{{{-y=-9*4}}}

{{{-y= -36}}}

{{{highlight(y= 36)}}}=>yellow jelly beans were originally in the dish

go to {{{r=3y/4}}}, substitute {{{36}}} for {{{y}}} 

 {{{r=(3*36)/4}}}

 {{{r=(3*cross(36)9)/cross(4)1}}}

 {{{r=3*9}}}

 {{{highlight(r=27)}}}=> red jelly beans were originally in the dish

check:
{{{r/y=3/4}}}
{{{27/36=3/4}}}
{{{27*4=3*36}}}
{{{108=108}}}



{{{(r-3)/(y-6)=4/5}}}
{{{(27-3)/(36-6)=4/5}}}
{{{24/30=4/5}}}

{{{24*5=4*30}}}

{{{120=120}}}