document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=761707>Question 761707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a:b=2:3, b:c=4:5, c:d= 6:7 so find a:b:c:d? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463427 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=463427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A . . . .2 . . . . .B . . . 4 . . . . . C . . . 6<BR>\n" );
document.write( "-- . = . --- . . . . -- . = . -- . . . . . -- .= .----<BR>\n" );
document.write( "B . . . .3 . . . . .C . . . 5 . . . . . D . . . 7\r<BR>\n" );
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document.write( "The best way I think I can explain this is first to find the LCM of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which, of course, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2A+5+%2A+7+=+105 ALIGN=MIDDLE  ALT=\"3+%2A+5+%2A+7+=+105\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now express each of the fractions above with a denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=105 ALIGN=MIDDLE  ALT=\"105\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2F+B+=+70+%2F+105 ALIGN=MIDDLE  ALT=\"A+%2F+B+=+70+%2F+105\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+%2F+C+=+84+%2F105 ALIGN=MIDDLE  ALT=\"B+%2F+C+=+84+%2F105\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+%2F+D+=+90+%2F+105 ALIGN=MIDDLE  ALT=\"C+%2F+D+=+90+%2F+105\"   DISABLED_style= \"max-width:90%; height:auto;\" > . . . . . . . . . ( 1 )\r<BR>\n" );
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document.write( "In the last ratio, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" >. How can we express <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+%2F+C ALIGN=MIDDLE  ALT=\"B+%2F+C\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2F+90 ALIGN=MIDDLE  ALT=\"x+%2F+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "Well, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+%2F+C+=+84+%2F+105 ALIGN=MIDDLE  ALT=\"B+%2F+C+=+84+%2F+105\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so if we want to express this as<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2F+90 ALIGN=MIDDLE  ALT=\"+x+%2F+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84+%2F+105+=+x+%2F+90 ALIGN=MIDDLE  ALT=\"84+%2F+105+=+x+%2F+90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+84+%2890+%2F+105%29+=+72 ALIGN=MIDDLE  ALT=\"x+=+84+%2890+%2F+105%29+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore we can express <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+%2F+C ALIGN=MIDDLE  ALT=\"B+%2F+C\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72+%2F+90 ALIGN=MIDDLE  ALT=\"72+%2F+90\"   DISABLED_style= \"max-width:90%; height:auto;\" > . . . . . . . . ( 2 )\r<BR>\n" );
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document.write( "We have that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2F+B+=+70+%2F+105 ALIGN=MIDDLE  ALT=\"A+%2F+B+=+70+%2F+105\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and now we want to get it so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72 ALIGN=MIDDLE  ALT=\"72\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70+%2F+105+=+y+%2F+72 ALIGN=MIDDLE  ALT=\"70+%2F+105+=+y+%2F+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+70+%2872+%2F+105%29+=+48 ALIGN=MIDDLE  ALT=\"y+=+70+%2872+%2F+105%29+=+48\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore we can express <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2F+B ALIGN=MIDDLE  ALT=\"A+%2F+B\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48+%2F+72 ALIGN=MIDDLE  ALT=\"48+%2F+72\"   DISABLED_style= \"max-width:90%; height:auto;\" > . . . . . . . . ( 3 )\r<BR>\n" );
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document.write( "Collecting the three ratios ( 1 ), ( 2 ) and ( 3 ) together, we have\r<BR>\n" );
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document.write( "A . . . 48 . . . . . B . . . .72 . . . . . C . . . 90<BR>\n" );
document.write( "-- . = . ---- . . . . --- . = . ---- . . . . . -- .= .-----<BR>\n" );
document.write( "B . . . 72 . . . . . C . . . .90 . . . . . D . . .105\r<BR>\n" );
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document.write( "From which you can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%3A+B+%3A+C+%3A+D+=+48+%3A+72+%3A+90+%3A+105 ALIGN=MIDDLE  ALT=\"A+%3A+B+%3A+C+%3A+D+=+48+%3A+72+%3A+90+%3A+105\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or, dividing by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you get in lowest terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%3A+B+%3A+C+%3A+D+=+16+%3A+24+%3A+30+%3A+35 ALIGN=MIDDLE  ALT=\"A+%3A+B+%3A+C+%3A+D+=+16+%3A+24+%3A+30+%3A+35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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