document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190259>Question 1190259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2/3 of the beads are red 1/4 are yellow and the rest are blue there are 42 more red beads then blue. How much beads are there in total? I know that the answer is 72. but the problem is I am told to solve it without using algebra. And I cannot find a way to solve it without using an unknown variable.    <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821859 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Add up the given fractions for red and yellow<BR>\n" );
document.write( "2/3 + 1/4<BR>\n" );
document.write( "8/12 + 3/12<BR>\n" );
document.write( "11/12\r<BR>\n" );
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document.write( "11/12 of all the beads are either red or yellow, but not both. <BR>\n" );
document.write( "The rest (1/12) are blue.\r<BR>\n" );
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document.write( "The fractional amounts of red and blue are<BR>\n" );
document.write( "8/12<BR>\n" );
document.write( "1/12<BR>\n" );
document.write( "in that order\r<BR>\n" );
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document.write( "Subtract those fractional amounts<BR>\n" );
document.write( "red - blue = 8/12 - 1/12 = 7/12\r<BR>\n" );
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document.write( "Then turn to the statement that there are \"42 more red beads then blue\", which is saying<BR>\n" );
document.write( "red = blue + 42<BR>\n" );
document.write( "that rearranges into the idea<BR>\n" );
document.write( "red - blue = 42<BR>\n" );
document.write( "I.e. the difference of the red and blue beads is 42\r<BR>\n" );
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document.write( "7/12 of the beads represents the difference of red and blue (42)<BR>\n" );
document.write( "So there are (12/7)*42 = 12*6 = 72 beads total.\r<BR>\n" );
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document.write( "Or note that (7/12)*72 = 42, which is the reverse flow of logic of the previous paragraph.<BR>\n" );
document.write( "(7/12)*(total) = difference in red and blue<BR>\n" );
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