Question 1108778


 let red marbles be {{{r}}}
let green and blue marbles  be {{{g}}} and {{{b}}} 
let the total number of marbles in the box be {{{m}}}

given:
{{{44}}}% or {{{0.44}}} of the marbles in a box are red: => {{{r=0.44m}}} ....eq.1

green and blue in the ratio of {{{5:3}}}: =>{{{g:b=5:3}}}

=>{{{3g=5b}}}

=>{{{b=3g/5}}}....eq.1a


the total number of marbles in the box will be: 

{{{m=r+g+b}}}

since there are {{{270}}} more red than green, and the number of green is 

{{{g=r-270}}} ....since {{{r=0.44m}}}, we have

{{{g=0.44m-270}}}...eq.2 

{{{m=r+g+b}}} substitute values from eq.1a and eq.2 

{{{m=0.44m+(0.44m-270)+3(0.44m-270)/5}}}...sole for {{{m}}}

{{{m=0.44m+0.44m-270+(1.32m-810)/5}}}

{{{m=0.44m+0.44m-270+1.32m/5-810/5}}}

{{{m=0.44m+0.44m-270+0.264m-162}}}

{{{m-0.44m-0.44m-0.264m=-270-162}}}

{{{-0.144m=-432}}}

{{{m=-432/-0.144}}}

{{{highlight(m=3000)}}}...=> the total number of marbles in the box



since {{{44}}}% or {{{0.44}}} of the marbles in a box are red, we have

{{{r=0.44*3000}}}

{{{highlight(r=1320)}}}

since there are {{{270}}} more red than green, we have

{{{g=1320-270}}}

{{{highlight(g=1050)}}}

what percentage ({{{x/100}}}) of the {{{3000}}} marbles are green:

{{{(x/100)3000=1050}}}

{{{30x=1050}}}

{{{x=1050/30}}}

{{{x=35}}} 

so, {{{highlight(35)}}}% of marbles are green


since the number of blue marbles is {{{b=3g/5}}}, we have 

{{{b=(3*1050)/5}}}

{{{b=3*210}}}

{{{highlight(b=630)}}}

so, we have {{{highlight(1320)}}} red ,{{{highlight(1050)}}} green, and  {{{highlight(630)}}} blue marbles in the box


check if green and blue are in the ratio of {{{5:3}}}:
{{{1050:630=5:3}}}
{{{1050*3=5*630}}}
{{{3150=3150}}} which is true