document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85077>Question 85077</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cashews costing $5.50 per pound are mixed with pecans costing $3.00 per pound.  How many pounds of each should be mixed to obtain a 20 pound cashew pecan mixture costing $3.50 per pound? \r<BR>\n" );
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document.write( "Thanks,<BR>\n" );
document.write( "Tonya  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #61303 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=61303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set up the following system of equations\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.5x%2B3y=20%2A3.50 ALIGN=MIDDLE  ALT=\"5.5x%2B3y=20%2A3.50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=20 ALIGN=MIDDLE  ALT=\"x%2By=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.5x%2B3y=70 ALIGN=MIDDLE  ALT=\"5.5x%2B3y=70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply the first equation by 10 to remove the decimal\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55x%2B30y=700 ALIGN=MIDDLE  ALT=\"55x%2B30y=700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=20 ALIGN=MIDDLE  ALT=\"x%2By=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solving_linear_system_by_elimination.solver>Solving a System of Linear Equations by Elimination/Addition</A></TD></TR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Lets start with the given system of linear equations<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax%2B30%2Ay=700 ALIGN=MIDDLE  ALT=\"55%2Ax%2B30%2Ay=700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%2B1%2Ay=20 ALIGN=MIDDLE  ALT=\"1%2Ax%2B1%2Ay=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa).<BR>\n" );
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document.write( "  So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero.<BR>\n" );
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document.write( "  So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 55 and 1 to some equal number, we could try to get them to the LCM.<BR>\n" );
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document.write( "  Since the LCM of 55 and 1 is 55, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -55 like this:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A%2855%2Ax%2B30%2Ay%29=%28700%29%2A1 ALIGN=MIDDLE  ALT=\"1%2A%2855%2Ax%2B30%2Ay%29=%28700%29%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the top equation (both sides) by 1<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-55%2A%281%2Ax%2B1%2Ay%29=%2820%29%2A-55 ALIGN=MIDDLE  ALT=\"-55%2A%281%2Ax%2B1%2Ay%29=%2820%29%2A-55\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the bottom equation (both sides) by -55<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  So after multiplying we get this:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax%2B30%2Ay=700 ALIGN=MIDDLE  ALT=\"55%2Ax%2B30%2Ay=700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-55%2Ax-55%2Ay=-1100 ALIGN=MIDDLE  ALT=\"-55%2Ax-55%2Ay=-1100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Notice how 55 and -55 add to zero (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2B-55=0 ALIGN=MIDDLE  ALT=\"55%2B-55=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Now add the equations together. In order to add 2 equations, group like terms and combine them<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2855%2Ax-55%2Ax%29%2B%2830%2Ay-55%2Ay%29=700-1100 ALIGN=MIDDLE  ALT=\"%2855%2Ax-55%2Ax%29%2B%2830%2Ay-55%2Ay%29=700-1100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2855-55%29%2Ax%2B%2830-55%29y=700-1100 ALIGN=MIDDLE  ALT=\"%2855-55%29%2Ax%2B%2830-55%29y=700-1100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2855%2B-55%29%2Ax%2B%2830-55%29%2Ay=700-1100 ALIGN=MIDDLE  ALT=\"cross%2855%2B-55%29%2Ax%2B%2830-55%29%2Ay=700-1100\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether.<BR>\n" );
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document.write( "  So after adding and canceling out the x terms we're left with:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25%2Ay=-400 ALIGN=MIDDLE  ALT=\"-25%2Ay=-400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-400%2F-25 ALIGN=MIDDLE  ALT=\"y=-400%2F-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25 ALIGN=MIDDLE  ALT=\"-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for y<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16 ALIGN=MIDDLE  ALT=\"y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Now plug this answer into the top equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax%2B30%2Ay=700 ALIGN=MIDDLE  ALT=\"55%2Ax%2B30%2Ay=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for x<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax%2B30%2816%29=700 ALIGN=MIDDLE  ALT=\"55%2Ax%2B30%2816%29=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16 ALIGN=MIDDLE  ALT=\"y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax%2B480=700 ALIGN=MIDDLE  ALT=\"55%2Ax%2B480=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax=700-480 ALIGN=MIDDLE  ALT=\"55%2Ax=700-480\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480 ALIGN=MIDDLE  ALT=\"480\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax=220 ALIGN=MIDDLE  ALT=\"55%2Ax=220\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the terms on the right side<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%281%2F55%29%2855%29%29%2Ax=%28220%29%281%2F55%29 ALIGN=MIDDLE  ALT=\"cross%28%281%2F55%29%2855%29%29%2Ax=%28220%29%281%2F55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F55 ALIGN=MIDDLE  ALT=\"1%2F55\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This will cancel out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55 ALIGN=MIDDLE  ALT=\"55\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the terms on the right side<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  So our answer is <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16 ALIGN=MIDDLE  ALT=\"y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  which also looks like<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Notice if we graph the equations (if you need help with graphing, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver</a>)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax%2B30%2Ay=700 ALIGN=MIDDLE  ALT=\"55%2Ax%2B30%2Ay=700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%2B1%2Ay=20 ALIGN=MIDDLE  ALT=\"1%2Ax%2B1%2Ay=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  we get <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++drawing%28+500%2C+600%2C+-14%2C+14%2C+-26%2C+26%2C%0D%0A++++graph%28+500%2C+600%2C+-14%2C+14%2C+-26%2C+26%2C+%28700-55%2Ax%29%2F30%2C+%2820-1%2Ax%29%2F1+%29%2C%0D%0A++++blue%28++circle%28+4%2C+16%2C+0.186666666666667+%29+%29+%0D%0A++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=55%2Ax%2B30%2Ay=700 ALIGN=MIDDLE  ALT=\"55%2Ax%2B30%2Ay=700\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ax%2B1%2Ay=20 ALIGN=MIDDLE  ALT=\"1%2Ax%2B1%2Ay=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle).<BR>\n" );
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document.write( "  and we can see that the two equations intersect at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" >). This verifies our answer.</TD></TR>\n" );
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document.write( "so you need 4 pounds of cashews and 16 pounds of pecans to make a 20 pound mix costing $3.50 per pound. </SPAN>\n" );
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