document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187121>Question 1187121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that S=7a+b+7c and also S=6a+8b+6c, where 51<S<149 and a, b, c and S are integers, find the sum a+b+c. A) 14  B) 15  C) 16  D) 17  E) 18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818066 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+7a%2Bb%2B7c ALIGN=MIDDLE  ALT=\"S+=+7a%2Bb%2B7c\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [1]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+6a%2B8b%2B6c ALIGN=MIDDLE  ALT=\"S+=+6a%2B8b%2B6c\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [2]<br><BR>\n" );
document.write( "Subtract [2] from [1]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-7b%2Bc+=+0 ALIGN=MIDDLE  ALT=\"a-7b%2Bc+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc+=+7b ALIGN=MIDDLE  ALT=\"a%2Bc+=+7b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+%28a%2Bc%29%2F7 ALIGN=MIDDLE  ALT=\"b+=+%28a%2Bc%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [3]<br><BR>\n" );
document.write( "Substitute [3] in [1]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+7a%2Bb%2B7c+=+7%28a%2Bc%29%2B%28a%2Bc%29%2F7+=+%2850%2F7%29%28a%2Bc%29+=+50%28%28a%2Bc%29%2F7%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We know a, b, and c are integers, so S is an integer.  From the last equation, we also know that S is a multiple of 50, and (a+c) is a multiple of 7.<br><BR>\n" );
document.write( "We also know that S is between 51 and 149.  The only multiple of 50 between 51 and 149 is 100.  So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+100+=+50%28%28a%2Bc%29%2F7%29 ALIGN=MIDDLE  ALT=\"S+=+100+=+50%28%28a%2Bc%29%2F7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bc%29%2F7=2 ALIGN=MIDDLE  ALT=\"%28a%2Bc%29%2F7=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc=14 ALIGN=MIDDLE  ALT=\"a%2Bc=14\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [4]<br><BR>\n" );
document.write( "Substitute [4] in [3]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+14%2F2+=+7 ALIGN=MIDDLE  ALT=\"b+=+14%2F2+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >  [5]<br><BR>\n" );
document.write( "Combine [4] and [5] to get the answer.<br><BR>\n" );
document.write( "ANSWER: a+b+c = 14+2 = 16 -- answer choice C<br><BR>\n" );
document.write( " </SPAN>\n" );
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