document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825463>Question 825463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A chemist wants to make 700mL of a 6% acid solution by using 5% and 12% acid solutions. How much of each should she use? \r<BR>\n" );
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document.write( "Please do not use system of equations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497314 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=497314\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "5x + 12y = 6*700<BR>\n" );
document.write( "x + y = 700<BR>\n" );
document.write( "---<BR>\n" );
document.write( "put the system of linear equations into standard form<BR>\n" );
document.write( "---<BR>\n" );
document.write( "5x + 12y = 4200<BR>\n" );
document.write( "x + y = 700<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above linear system in standard form into this matrix-method solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer by matrix method:<BR>\n" );
document.write( "x = 600 mL of 5%<BR>\n" );
document.write( "y = 100 mL of 12%<BR>\n" );
document.write( "---<BR>\n" );
document.write( "system matrix<BR>\n" );
document.write( "5 12<BR>\n" );
document.write( "1 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "inverse of system matrix<BR>\n" );
document.write( "-0.14285714 1.7142857<BR>\n" );
document.write( "0.14285714 -0.71428571<BR>\n" );
document.write( "---<BR>\n" );
document.write( "determinant of system matrix = -7<BR>\n" );
document.write( "---<BR>\n" );
document.write( "now solve by elimination:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "5x + 12y = 4200<BR>\n" );
document.write( "(x + y = 700)*(-5)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "5x + 12y = 4200<BR>\n" );
document.write( "-5x - 5y = -3500<BR>\n" );
document.write( "---<BR>\n" );
document.write( "add the system:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "7y = 700<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 100<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x + y = 700<BR>\n" );
document.write( "x = 700 - y<BR>\n" );
document.write( "x = 700 - 100<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = 600<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer by elimination method:<BR>\n" );
document.write( "x = 600 mL of 5%<BR>\n" );
document.write( "y = 100 mL of 12%<BR>\n" );
document.write( "---<BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "the answer by the matrix method agrees with the answer by the elimination method.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 4-equations 4-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );