document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=873614>Question 873614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The denominators of two fractions are consecutive natural numbers. Both fractions are in their lowest terms. Their sum is 51/56. Find the greater of these two fractions.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #527007 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=527007\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The denominators of two fractions are consecutive natural numbers. Both fractions are in their lowest terms. Their sum is 51/56. Find the greater of these two fractions. <BR>\n" );
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document.write( "Let a = numerator of the 1st fraction<BR>\n" );
document.write( "let b = numerator of the 2nd fraction<BR>\n" );
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document.write( "Regarding the denominator, only two consecutive numbers are factors of 56<BR>\n" );
document.write( "So we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F7 ALIGN=MIDDLE  ALT=\"a%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F8 ALIGN=MIDDLE  ALT=\"b%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51%2F56 ALIGN=MIDDLE  ALT=\"51%2F56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "common denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288a%29%2F56 ALIGN=MIDDLE  ALT=\"%288a%29%2F56\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287b%29%2F56 ALIGN=MIDDLE  ALT=\"%287b%29%2F56\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51%2F56 ALIGN=MIDDLE  ALT=\"51%2F56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we can say<BR>\n" );
document.write( "8a + 7b = 51<BR>\n" );
document.write( "8a = -7b + 51<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F8 ALIGN=MIDDLE  ALT=\"-7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >b + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51%2F8 ALIGN=MIDDLE  ALT=\"51%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "only one integer solution to this equation, b=5, find a<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%2F8 ALIGN=MIDDLE  ALT=\"-7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >(5) + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51%2F8 ALIGN=MIDDLE  ALT=\"51%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-35%2F8 ALIGN=MIDDLE  ALT=\"-35%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=51%2F8 ALIGN=MIDDLE  ALT=\"51%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F8 ALIGN=MIDDLE  ALT=\"16%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 2<BR>\n" );
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document.write( "Our fractions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F7 ALIGN=MIDDLE  ALT=\"2%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > & <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8 ALIGN=MIDDLE  ALT=\"5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is the greatest<BR>\n" );
document.write( " </SPAN>\n" );
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