document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131188>Question 1131188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of three numbers is 15.  The sum of twice the first&#8203; number, 4 times the second&#8203; number, and 5 times the third number is 49.  The difference between 3 times the first number and the second number is 16.  Find the three numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747815 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=747815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of three numbers is 15.<BR>\n" );
document.write( "a + b + c = 15<BR>\n" );
document.write( " The sum of twice the first&#8203; number, 4 times the second&#8203; number, and 5 times the third number is 49.<BR>\n" );
document.write( "2a + 4b + 5c = 49<BR>\n" );
document.write( " The difference between 3 times the first number and the second number is 16.<BR>\n" );
document.write( "3a - b = 16<BR>\n" );
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document.write( " Find the three numbers.<BR>\n" );
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document.write( "Add the 1st and the 3rd equations<BR>\n" );
document.write( "a + b + c = 15<BR>\n" );
document.write( "3a -b + 0 = 16<BR>\n" );
document.write( "-----------------adding eliminates b<BR>\n" );
document.write( "4a + 0 + c = 31<BR>\n" );
document.write( "4a + c = 31<BR>\n" );
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document.write( "multiply the 1st equation by 4 and subtract the 2nd equation<BR>\n" );
document.write( "4a + 4b + 4c = 60<BR>\n" );
document.write( "2a + 4b + 5c = 49<BR>\n" );
document.write( "-------------------subtraction eliminates b<BR>\n" );
document.write( "2a + 0 - c = 11<BR>\n" );
document.write( "2a - c = 11<BR>\n" );
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document.write( "Add the two resulting equations<BR>\n" );
document.write( "4a + c = 31<BR>\n" );
document.write( "2a - c = 11<BR>\n" );
document.write( "----------------adding eliminates c, find a<BR>\n" );
document.write( "6a + 0 = 42<BR>\n" );
document.write( "a = 42/6<BR>\n" );
document.write( "a = 7<BR>\n" );
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document.write( "use the 3rd equation to find b<BR>\n" );
document.write( "3a - b = 16<BR>\n" );
document.write( "3(7) - b = 16<BR>\n" );
document.write( "-b = 16 - 21<BR>\n" );
document.write( "-b = -5<BR>\n" );
document.write( "b = 5<BR>\n" );
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document.write( "Find c using the 1st equation<BR>\n" );
document.write( "7 + 5 + c = 15<BR>\n" );
document.write( "c = 15 - 12<BR>\n" );
document.write( "c = 3<BR>\n" );
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document.write( "Chck solutions in the 2nd equation<BR>\n" );
document.write( "2(7) + 4(5) + 5(3) = <BR>\n" );
document.write( "14 + 20 + 15 = 49<BR>\n" );
document.write( "  </SPAN>\n" );
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