document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252666>Question 252666</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a and b are different positive integers, and 5a + 2b = 34 is an integer,<BR>\n" );
document.write( "what is the sum of all possible values of a?\r<BR>\n" );
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document.write( "A) 6  B) 10   C) 12   D) 14   E) 16 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184696 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5a+2b=34<BR>\n" );
document.write( "Answers could be a=6 and b=2<BR>\n" );
document.write( "2b must be even but b can be even or odd.<BR>\n" );
document.write( "so if 2b must be even then 5a must be even so a must be even since 5 is odd and 34 is even.<BR>\n" );
document.write( "If you subtract an even number from an even number, you get an even number.<BR>\n" );
document.write( "a must be less than 7 since 5*7=35 and both a and b must be positive.<BR>\n" );
document.write( "But the answers are sums of a not a itself<BR>\n" );
document.write( "10 is possible because 5*4+2*7=34<BR>\n" );
document.write( "6+4=10\r<BR>\n" );
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document.write( "5*2+2*12=34<BR>\n" );
document.write( "so we could have 6,4 and 2 for a total of 12<BR>\n" );
document.write( "since 6, 4 and 2 are possible values for a 14 can't be since it would need 2 twice.<BR>\n" );
document.write( "16 has a similar problem with 4<BR>\n" );
document.write( "since we already have a sum of 12 a sum of 16 would need 4 again.<BR>\n" );
document.write( "so the highest sum possible for a would be 12 using 2,4 and 6. We could also have a =0  and b would equal 17 but the sum of the a's would not change.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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