document.write( "Question 1180265: There are some green, red and blue buttons in a box. 1/2 of the buttons are green and 1/3 of the buttons are blue. The difference between the number of green and red buttons is 20.
\n" ); document.write( "a) What fraction of the buttons are red?
\n" ); document.write( "b) How many buttons are there altogether? \n" ); document.write( "
Algebra.Com's Answer #809873 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
let n be the number of buttons in the box.
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\n" ); document.write( "\n" ); document.write( "There are some green, red and blue buttons in a box. \r
\n" ); document.write( "\n" ); document.write( "\"G+%2B+R+%2B+B+=+n\"\r
\n" ); document.write( "\n" ); document.write( "1/2 of the buttons are green \r
\n" ); document.write( "\n" ); document.write( "\"G+=+expr%281%2F2%29n\"\r
\n" ); document.write( "\n" ); document.write( "and 1/3 of the buttons are blue. \r
\n" ); document.write( "\n" ); document.write( "\"B+=+expr%281%2F3%29n\"\r
\n" ); document.write( "\n" ); document.write( "The difference between the number of green and red buttons is 20.\r
\n" ); document.write( "\n" ); document.write( "\"G+-+R+=+20\"
\n" ); document.write( "\"G-20=R\"
\n" ); document.write( "\"expr%281%2F2%29n-20=R\"
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Substitute for G, R and B in\r\n" );
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document.write( "\"G+%2B+R+%2B+B+=+n\"\r\n" );
document.write( "\"expr%281%2F2%29n%2B%28expr%281%2F2%29n-20%29%2Bexpr%281%2F3%29n=n\" \r\n" );
document.write( "\"expr%281%2F2%29n%2Bexpr%281%2F2%29n-20%2Bexpr%281%2F3%29n=n\"\r\n" );
document.write( "\"3n%2B3n-120%2B2n=6n\"\r\n" );
document.write( "\"8n-120=6n\"\r\n" );
document.write( "\"2n=120\"\r\n" );
document.write( "\"n=60\"\r\n" );
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We answer the b) part first:

\n" ); document.write( "b) How many buttons are there altogether?
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document.write( "60 buttons altogether.\r\n" );
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document.write( "\"G+=+expr%281%2F2%29n\"\r\n" );
document.write( "\"G+=+expr%281%2F2%2960\"\r\n" );
document.write( "\"G+=+30\"\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "\"G-20=R\"\r\n" );
document.write( "\"30-20=R\"\r\n" );
document.write( "\"10=R\"\r\n" );
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a) What fraction of the buttons are red?
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document.write( "IOW, what fraction of 60 buttons is 10 red buttons?\r\n" );
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document.write( "Answer = 10/60 = 1/6\r\n" );
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document.write( "Edwin
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