document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825251>Question 825251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following problem using Elimination method.\r<BR>\n" );
document.write( "\n" );
document.write( "1. how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution?\r<BR>\n" );
document.write( "\n" );
document.write( "2. an airplane flying in the same direction as the wind can cover a certain distance in 2hrs. the return trip is against the direction of wind and takes 2.5 hrs. what are the speeds of the wind and the plane, if the one-way distance is 960km?\r<BR>\n" );
document.write( "\n" );
document.write( "3. it takes a boat 2hrs to travel 24km downstream and 3hrs to travel 18km upstream. what are the speeds of the boat in still water and of the current  of the river? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #497163 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=497163\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "This post contains three different questions.<BR>\n" );
document.write( "I will answer the first question.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "question:<BR>\n" );
document.write( "How many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = gallons of 20% solution<BR>\n" );
document.write( "y = gallons of 50% solution<BR>\n" );
document.write( "---<BR>\n" );
document.write( "20x + 50y = 30*9<BR>\n" );
document.write( "x + y = 9<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( "20x + 50y = 270<BR>\n" );
document.write( "x + y = 9<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( "solution by matrix method:<BR>\n" );
document.write( "x = gallons of 20% solution = 6<BR>\n" );
document.write( "y = gallons of 50% solution = 3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "system matrix<BR>\n" );
document.write( "20 50<BR>\n" );
document.write( "1 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "inverse of system matrix<BR>\n" );
document.write( "-0.033333333 1.6666667<BR>\n" );
document.write( "0.033333333 -0.66666667<BR>\n" );
document.write( "---<BR>\n" );
document.write( "determinant of system matrix = -30<BR>\n" );
document.write( "---<BR>\n" );
document.write( "now the solution by elimination:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "20x + 50y = 270<BR>\n" );
document.write( "(x + y = 9)*(-20)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "20x + 50y = 270<BR>\n" );
document.write( "-20x - 20y = -180<BR>\n" );
document.write( "---<BR>\n" );
document.write( "add the system:<BR>\n" );
document.write( "30y = 90<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = 3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x + y = 9<BR>\n" );
document.write( "x + 3 = 9<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "---<BR>\n" );
document.write( "solution by elimination method:<BR>\n" );
document.write( "x = gallons of 20% solution = 6<BR>\n" );
document.write( "y = gallons of 50% solution = 3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "solution by matrix method agrees with solution by 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 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );