document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209283>Question 1209283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 1/a + 1/b = 5/12 and ab = 24, what is the value of a+b? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848099 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=848099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are at least three ways to answer this question. \r<BR>\n" );
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document.write( "Method 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa+%2B+1%2Fb+=+5%2F12 ALIGN=MIDDLE  ALT=\"1%2Fa+%2B+1%2Fb+=+5%2F12\"   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%28ab%29+%2B+a%2F%28ab%29+=+10%2F24 ALIGN=MIDDLE  ALT=\"b%2F%28ab%29+%2B+a%2F%28ab%29+=+10%2F24\"   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=%28b+%2B+a%29%2F%28ab%29+=+10%2F24 ALIGN=MIDDLE  ALT=\"%28b+%2B+a%29%2F%28ab%29+=+10%2F24\"   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=%28a%2Bb%29%2F%2824%29+=+10%2F24 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%2F%2824%29+=+10%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in ab = 24.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb+=+10 ALIGN=MIDDLE  ALT=\"a%2Bb+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Method 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa+%2B+1%2Fb+=+5%2F12 ALIGN=MIDDLE  ALT=\"1%2Fa+%2B+1%2Fb+=+5%2F12\"   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=ab%2A%281%2Fa+%2B+1%2Fb%29+=+ab%2A%285%2F12%29 ALIGN=MIDDLE  ALT=\"ab%2A%281%2Fa+%2B+1%2Fb%29+=+ab%2A%285%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by ab\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%2A%281%2Fa%29+%2B+ab%2A%281%2Fb%29+=+ab%2A%285%2F12%29 ALIGN=MIDDLE  ALT=\"ab%2A%281%2Fa%29+%2B+ab%2A%281%2Fb%29+=+ab%2A%285%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+%2B+a+=+ab%2A%285%2F12%29 ALIGN=MIDDLE  ALT=\"b+%2B+a+=+ab%2A%285%2F12%29\"   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=a%2Bb+=+24%2A%285%2F12%29 ALIGN=MIDDLE  ALT=\"a%2Bb+=+24%2A%285%2F12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in ab = 24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb+=+10 ALIGN=MIDDLE  ALT=\"a%2Bb+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Method 3\r<BR>\n" );
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document.write( "ab = 24 rearranges to b = 24/a which has reciprocal 1/b = a/24\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa+%2B+1%2Fb+=+5%2F12 ALIGN=MIDDLE  ALT=\"1%2Fa+%2B+1%2Fb+=+5%2F12\"   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=1%2Fa+%2B+a%2F24+=+5%2F12 ALIGN=MIDDLE  ALT=\"1%2Fa+%2B+a%2F24+=+5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replaced 1/b with a/24\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fa+%2B+a%2F24%29%2A24a+=+%285%2F12%29%2A24a ALIGN=MIDDLE  ALT=\"%281%2Fa+%2B+a%2F24%29%2A24a+=+%285%2F12%29%2A24a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD 24a to clear out the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fa%29%2A24a+%2B+%28a%2F24%29%2A24a+=+10a ALIGN=MIDDLE  ALT=\"%281%2Fa%29%2A24a+%2B+%28a%2F24%29%2A24a+=+10a\"   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=24+%2B+a%5E2+=+10a ALIGN=MIDDLE  ALT=\"24+%2B+a%5E2+=+10a\"   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=a%5E2-10a%2B24+=+0 ALIGN=MIDDLE  ALT=\"a%5E2-10a%2B24+=+0\"   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=%28a-6%29%28a-4%29+=+0 ALIGN=MIDDLE  ALT=\"%28a-6%29%28a-4%29+=+0\"   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=a-6=0 ALIGN=MIDDLE  ALT=\"a-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-4=0 ALIGN=MIDDLE  ALT=\"a-4=0\"   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=a+=+6 ALIGN=MIDDLE  ALT=\"a+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+4 ALIGN=MIDDLE  ALT=\"a+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If a = 6, then b = 24/a = 24/6 = 4.<BR>\n" );
document.write( "If a = 4, then b = 24/a = 24/4 = 6.<BR>\n" );
document.write( "The order of a,b doesn't matter so we arrive at the same pairing.\r<BR>\n" );
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document.write( "The pair of values is a = 4 and b = 6 (or a = 6 and b = 4).<BR>\n" );
document.write( "As a way to check, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fa+%2B+1%2Fb+=+1%2F4+%2B+1%2F6+=+3%2F12+%2B+2%2F12+=+%283%2B2%29%2F12+=+5%2F12 ALIGN=MIDDLE  ALT=\"1%2Fa+%2B+1%2Fb+=+1%2F4+%2B+1%2F6+=+3%2F12+%2B+2%2F12+=+%283%2B2%29%2F12+=+5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In short <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4+%2B+1%2F6+=+5%2F12 ALIGN=MIDDLE  ALT=\"1%2F4+%2B+1%2F6+=+5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > which helps us confirm we have the correct a,b values.\r<BR>\n" );
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document.write( "Then a+b = 4+6 = <font color=red>10</font>\r<BR>\n" );
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document.write( "Answer: <font color=red>10</font><BR>\n" );
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