document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=306388>Question 306388</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Combined there are 202 Asians, African, Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by 71. The difference between the number of Europeans and Americans is 16. If the number of Africans is doubled, their population exceeds the number of Europeans and Americans by 18. Determine the number of Asians, Africans, Europeans, and Americans in this village. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #219711 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=219711\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Combined there are 202 Asians, African, Europeans, and Americans in a village. The number of Asians exceeds the number of Africans and Europeans by 71. The difference between the number of Europeans and Americans is 16. If the number of Africans is doubled, their population exceeds the number of Europeans and Americans by 18. Determine the number of Asians, Africans, Europeans, and Americans in this village.\r<BR>\n" );
document.write( "\n" );
document.write( " A +  F + E +  M    = 202<BR>\n" );
document.write( " A -  F - E + 0M    =  71<BR>\n" );
document.write( "0A + 0F + E -  M    =  16 --> E = M + 16 (substitute in)<BR>\n" );
document.write( "0A + 2F - E -  M    =  18<BR>\n" );
document.write( "to get<BR>\n" );
document.write( " A +  F + M + 16 +  M = 202<BR>\n" );
document.write( " A -  F - M - 16 + 0M =  71<BR>\n" );
document.write( "0A + 2F - M - 16 -  M =  18<BR>\n" );
document.write( "or<BR>\n" );
document.write( " A +  F + 2M = 186<BR>\n" );
document.write( " A -  F -  M =  87<BR>\n" );
document.write( "0A + 2F - 2M =  34 --> F - M = 17 --> F = M + 17 (substitute in)<BR>\n" );
document.write( "to get<BR>\n" );
document.write( " A +  M + 17 + 2M = 186<BR>\n" );
document.write( " A -  M - 17 -  M =  87<BR>\n" );
document.write( "or<BR>\n" );
document.write( " A + 3M = 169<BR>\n" );
document.write( " A - 2M = 104  (picked this one of the 2 to multiply by -1 and add to other)<BR>\n" );
document.write( "to get<BR>\n" );
document.write( " A + 3M =  169<BR>\n" );
document.write( "-A + 2M = -104 (add to one above)<BR>\n" );
document.write( "to get<BR>\n" );
document.write( " 0A + 5M =   65 --> M = 13 (number of Americans is 13)(plug into 2nd)<BR>\n" );
document.write( "- A + 2M = -104<BR>\n" );
document.write( "to get<BR>\n" );
document.write( "- A + 26 = -104<BR>\n" );
document.write( "or<BR>\n" );
document.write( "  A - 26 = 104 --> A = 130 (number of Asians is 130)<BR>\n" );
document.write( "now you got from A + F + E + M = 202<BR>\n" );
document.write( "130 + F + E + 13 = 202 <BR>\n" );
document.write( "this<BR>\n" );
document.write( "F + E + 143 = 202 --> F + E = 59<BR>\n" );
document.write( "we know from above E = M + 16 so E = 13 + 16 = 29 (number of Europeans is 29)<BR>\n" );
document.write( "so<BR>\n" );
document.write( "F + 29 = 59 --> F = 30 (number of Africans is 30)<BR>\n" );
document.write( "then<BR>\n" );
document.write( " A  +  F + E  +  M    = 202<BR>\n" );
document.write( "130 + 30 + 29 + 13    = (A + F) + (E + M) = 160 + 42 = 202<BR>\n" );
document.write( "Thus ends this difficult system of equations and substitution problem, hope this helps someone.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );