document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176875>Question 1176875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer has several packages of fertilizer for his new grain crop. The old packages contain 60 pounds of long-term growth supplement and 50 pounds of weed killer. The new packages contain 45 pounds of long-term growth supplement and 65 pounds of weed killer. Using past experiences, the farmer estimates that he needs 1350 pounds of long-term growth supplement and 1400 pounds of weed killer for the fields. How many old packages of fertilizer and how many new packages of fertilizer should he use?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #804861 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=804861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of old packages and y = the number of new packages.\r<BR>\n" );
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document.write( "create a table as shown below:\r<BR>\n" );
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document.write( "                                          x                y\r\n" );
document.write( "description                              old              new         total\r\n" );
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document.write( "long term growth supplements              60               45          1350\r\n" );
document.write( "weed killer                               50               65          1400\r\n" );
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document.write( "the two equations that need to be solved simultaneously are:\r<BR>\n" );
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document.write( "60x + 45y = 1350<BR>\n" );
document.write( "50x + 65y = 1400\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 5 and both sides of the second equation by 6 to get:\r<BR>\n" );
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document.write( "300x + 225y = 6750<BR>\n" );
document.write( "300x + 390y = 8400\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "165y = 1650\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = 1650 / 165 = 10\r<BR>\n" );
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document.write( "solve for x in the first equation to get:\r<BR>\n" );
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document.write( "300x + 225 * 10 = 6750<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = (6750 - 2250) / 300 = 4500 / 300 = 15\r<BR>\n" );
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document.write( "you have x = 15 and y = 10\r<BR>\n" );
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document.write( "go back to the original equations and replace x and y with these values to get:\r<BR>\n" );
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document.write( "60x + 45y = 1350 becomes 60 * 15 + 45 * 10 = 1350 which becomes 900 + 450 = 1350 which becomes 1350 = 1350 which is true.\r<BR>\n" );
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document.write( "50x + 65y = 1400 becomes 50 * 15 + 65 * 10 = 1400 which becomes 750 + 650 = 1400 which becomes 1400 = 1400 which is true.\r<BR>\n" );
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document.write( "the values of x and y are confirmed to be good.\r<BR>\n" );
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document.write( "your solution is that he should use 15 old packages and 10 new packages.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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