document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159558>Question 159558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ten 6.0-V and 12-V batteries have a total voltage of 84 V.How many of each type are there ??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117654 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=117654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> total voltage is 84.<BR>\n" );
document.write( "total number of batteries is 10.<BR>\n" );
document.write( "let x = number of 6 volt batteries.<BR>\n" );
document.write( "let y = number of 12 volt batteries.<BR>\n" );
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document.write( "x + y = 10<BR>\n" );
document.write( "6*x + 12*y = 84<BR>\n" );
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document.write( "first equation provides number of batteries in total.<BR>\n" );
document.write( "second equation provides number of volts in total.<BR>\n" );
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document.write( "in the first equation you can solve for x or y.  we'll solve for x.  <BR>\n" );
document.write( "subtract y from both sides of the equation.<BR>\n" );
document.write( "equation becomes x = 10 - y.<BR>\n" );
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document.write( "substitute (10 - y) for x in the second equation to remove one of the unknowns and equation becomes 6*(10-y) + 12*y = 84<BR>\n" );
document.write( "which becomes 60 - 6*y + 12*y = 84<BR>\n" );
document.write( "which becomes 60 + 6*y = 84<BR>\n" );
document.write( "subtract 60 from both sides of the equation and it becomes 6*y = 84 - 60<BR>\n" );
document.write( "which becomes 6*y = 24<BR>\n" );
document.write( "divide both sides of the equation by 6 and it becomes y = (24/6)<BR>\n" );
document.write( "which becomes y = 4<BR>\n" );
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document.write( "substitute 4 for y in the first equation<BR>\n" );
document.write( "it becomes x + 4 = 10<BR>\n" );
document.write( "subtract 4 from both sides of the equation and it becomes x = 6<BR>\n" );
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document.write( "answer appears to be<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "y = 4<BR>\n" );
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document.write( "substitute 6 for x and 4 for y in the first equation and it becomes 6 + 4 = 10 which becomes 10 = 10 meaning x and y look to be good values in the first equation.  that's not enough though.  they have to good values for both equations.<BR>\n" );
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document.write( "substitute 6 for x and 4 for y in the second equation and it becomes 6*6 + 4*12 = 84 which becomes 36 + 48 = 84 which becomes 84 = 84 meaning x and y look to be good values in the second equation as well.<BR>\n" );
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document.write( "answer is x = 6 and y = 4.<BR>\n" );
document.write( "x represents the number of 6 volt batteries.<BR>\n" );
document.write( "y represents the number of 12 volt batteries. <BR>\n" );
document.write( " </SPAN>\n" );
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