document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70769>Question 70769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm lost with this question. Can you help?\r<BR>\n" );
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document.write( "One side of a triangle is 2/3rds as long as the second side and the second side is 2/3rds as long as the third side. The perimeter = 95cm. What is the length of the longest side?\r<BR>\n" );
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document.write( "Would the equation be:\r<BR>\n" );
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document.write( "95 = X + (X x 2/3) + (X x 2/3)2/3\r<BR>\n" );
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document.write( "Is X the longest side and how do I find X?<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 #50537 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> My apologies. For some reason this answer became scrambled when I posted it, and I'm having a difficult time getting it corrected.  Until I do, maybe you can sort your way through it and get enough of a clue to work it out.  The error starts just after the line about dividing 95 by 19/5. Sorry for the mix up. \r<BR>\n" );
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document.write( "Your equation will work, it's just the algebraic manipulations that are hanging you up.\r<BR>\n" );
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document.write( "So let's go through the steps to crank out the answer.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+%2B+%28X+%2A+2%2F3%29+%2B+%28X+%2A+2%2F3%29%2A%282%2F3%29+=+95 ALIGN=MIDDLE  ALT=\"X+%2B+%28X+%2A+2%2F3%29+%2B+%28X+%2A+2%2F3%29%2A%282%2F3%29+=+95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's multiply out the third term on the left side.  By arithmetic rules when you multiply\r<BR>\n" );
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document.write( "two fractions you multiply their numerators and denominators. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3%2A2%2F3+=+4%2F9 ALIGN=MIDDLE  ALT=\"2%2F3%2A2%2F3+=+4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and the third term becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28X%2A4%29%2F9%29 ALIGN=MIDDLE  ALT=\"%28X%2A4%29%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This makes the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X+%2B+%28X+%2A+2%2F3%29+%2B+%28X%2A4%29%2F9+=+95 ALIGN=MIDDLE  ALT=\"X+%2B+%28X+%2A+2%2F3%29+%2B+%28X%2A4%29%2F9+=+95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "But before we can add the terms on the left side, we need a common denominator. You can\r<BR>\n" );
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document.write( "see that 9 would be a common denominator because 3 is a factor of it.  So let's multiply the\r<BR>\n" );
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document.write( "first term on the left by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F9 ALIGN=MIDDLE  ALT=\"9%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the second term on the left by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3 ALIGN=MIDDLE  ALT=\"3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "[This in effect is multiplying each of the terms by 1.] We don't have to do anything to\r<BR>\n" );
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document.write( "the third term because it already has the common denominator of 9.  After these manipulations\r<BR>\n" );
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document.write( "the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2AX%2F9+%2B+6%2AX%2F9+%2B+4%2AX%2F9+=+95 ALIGN=MIDDLE  ALT=\"9%2AX%2F9+%2B+6%2AX%2F9+%2B+4%2AX%2F9+=+95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Because the three terms on the left side have a common denominator, you can combine them\r<BR>\n" );
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document.write( "by adding the numerators and placing the sum over the common denominator.  If you add\r<BR>\n" );
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document.write( "the numerators the result is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2AX+%2B+6%2AX+%2B+4%2AX+=+19%2AX ALIGN=MIDDLE  ALT=\"9%2AX+%2B+6%2AX+%2B+4%2AX+=+19%2AX\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When you place this result over\r<BR>\n" );
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document.write( "the common denominator you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2819%2AX%29%2F9+=+95%7D%7D%0D%0A.%0D%0ANow+all+you+have+to+do+is+divide+both+sides+by+the+coefficient+of+X+which+is+%7B%7B%7B19%2F9 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This division causes the left side to become just X.\r<BR>\n" );
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document.write( "For dividing the 95 by 19/5 use the rule that to divide by a fraction invert it and multiply.<BR>\n" );
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document.write( "So 95 divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2F9 ALIGN=MIDDLE  ALT=\"19%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=95+%2A+%289%2F19 ALIGN=MIDDLE  ALT=\"95+%2A+%289%2F19\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Note that 19 goes into 95 5 times so the answer to this division is  5*9 = 45.<BR>\n" );
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document.write( "The answer to this problem is that the long side is 45.  If you back solve using this answer\r<BR>\n" );
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document.write( "you will find that the other two sides are 30 and 20 and the three sides do add up to 95.<BR>\n" );
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document.write( "Hope this helps.\r<BR>\n" );
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