Question 1180265
<pre>let n be the number of buttons in the box.</pre>

There are some green, red and blue buttons in a box. 

{{{G + R + B = n}}}

1/2 of the buttons are green 

{{{G = expr(1/2)n}}}

and 1/3 of the buttons are blue. 

{{{B = expr(1/3)n}}}

The difference between the number of green and red buttons is 20.

{{{G - R = 20}}}
{{{G-20=R}}}
{{{expr(1/2)n-20=R}}}
<pre>Substitute for G, R and B in

{{{G + R + B = n}}}
{{{expr(1/2)n+(expr(1/2)n-20)+expr(1/3)n=n}}} 
{{{expr(1/2)n+expr(1/2)n-20+expr(1/3)n=n}}}
{{{3n+3n-120+2n=6n}}}
{{{8n-120=6n}}}
{{{2n=120}}}
{{{n=60}}}

<pre>We answer the b) part first:</pre></pre>
b) How many buttons are there altogether?<pre>
60 buttons altogether.

{{{G = expr(1/2)n}}}
{{{G = expr(1/2)60}}}
{{{G = 30}}}

Substitute in 

{{{G-20=R}}}
{{{30-20=R}}}
{{{10=R}}}
</pre>a)      What fraction of the buttons are red?<pre>
IOW, what fraction of 60 buttons is 10 red buttons?

Answer = 10/60 = 1/6

Edwin</pre>