document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316441>Question 316441</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Restaurant owner want to purchase 250 sets of dishes.  He has two designs, one $20 & $45.  I have $6800 to spend.  How many of each designs should I order? Please show step by step solutions for x & y.  x = $20 y = $45  Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #226495 by </B><A HREF=/tutors/aboutme.mpl?userid=moshiz08><B>moshiz08(60)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=moshiz08><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=moshiz08><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=226495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x=the number of $20 dishes <BR>\n" );
document.write( "y=the number of $45 dishes \r<BR>\n" );
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document.write( "Since you want to purchase 250 total, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+250 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+250\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can rewrite this as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+250+-+x+ ALIGN=MIDDLE  ALT=\"y+=+250+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. (eq1) \r<BR>\n" );
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document.write( "Now suppose you buy 4 of the $20 dishes and 2 of the $45 dishes. The you spend 4*$20 = $80 on the four $20 dishes and 2*$45= $90 on the two $45 dollar dishes. \r<BR>\n" );
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document.write( "In general, you multiply. So if you buy x dishes for $20, you spend 20*x dollars on them. Then if you buy y dishes for $45, you spend 45*y on them. The total amount of money you spend is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x+%2B+45y ALIGN=MIDDLE  ALT=\"20x+%2B+45y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and since we know that you have $6800, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20x+%2B+45y+=+6800+ ALIGN=MIDDLE  ALT=\"+20x+%2B+45y+=+6800+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. (eq2) \r<BR>\n" );
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document.write( "Let us substitute our equation for y given by (eq1) into (eq2). \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20x+%2B+45y+=+20x+%2B+45%28250-x%29+=+6800+ ALIGN=MIDDLE  ALT=\"+20x+%2B+45y+=+20x+%2B+45%28250-x%29+=+6800+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x+%2B+45%28250-x%29+=+6800+ ALIGN=MIDDLE  ALT=\"20x+%2B+45%28250-x%29+=+6800+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Distributing the 45 gives \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x+%2B+11250+-45x+=+6800+ ALIGN=MIDDLE  ALT=\"20x+%2B+11250+-45x+=+6800+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Combining like terms gives \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25+x+%2B+11250+=+6800 ALIGN=MIDDLE  ALT=\"-25+x+%2B+11250+=+6800\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 25x to both sides to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+11250+=+6800+%2B+25x+ ALIGN=MIDDLE  ALT=\"+11250+=+6800+%2B+25x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Subtract 6800 from both sides to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4450+=+25x+ ALIGN=MIDDLE  ALT=\"4450+=+25x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Divide both sides by 25 to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+178+=+x+ ALIGN=MIDDLE  ALT=\"+178+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Thus, from (eq1) we can get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+250+-+x+=+250+-+178+=+72 ALIGN=MIDDLE  ALT=\"y+=+250+-+x+=+250+-+178+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So you should buy 178 of the $20 dish sets and you should buy 72 of the $45 dish sets. \r<BR>\n" );
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document.write( "Now let us check. The total number of dish sets you buy is 178 + 72 which is a total of 250 as you requested. The amount of money you pay is a total of 178 * $20 = $ 3560 for the $20 dishes and 72 * $45 = $3240 for the $45 dishes. This means you spend $3560 + $3240 = $6800.  </SPAN>\n" );
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