document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033759>Question 1033759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A printing facility prints and packages baseball cards. In April, they package the cards<BR>\n" );
document.write( "so that each pack has 20% star players and 80% journeymen. In May, each pack contains<BR>\n" );
document.write( "35% star players. A national retailer places an order for 10,000 packs, and wants them to<BR>\n" );
document.write( "average 26% star players. How many packs from each month should the printing<BR>\n" );
document.write( "facility include? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648408 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=648408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> order for 10,000 packs.<BR>\n" );
document.write( "some packs will have 20% star players.<BR>\n" );
document.write( "some packs will have 35% star players.<BR>\n" );
document.write( "average for the 10,000 packs needs to be 26% star players.\r<BR>\n" );
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document.write( "each pack will have 20% or 35%.<BR>\n" );
document.write( "the overall average of star players has to be 26% star players.<BR>\n" );
document.write( "this means that the order of 10,000 players has to contain 2600 star players.\r<BR>\n" );
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document.write( "let x equal the number of 20% packs.<BR>\n" );
document.write( "let y equal the number of 35% packs.\r<BR>\n" );
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document.write( "x + y = 10,000<BR>\n" );
document.write( "this tells you that the order must contain 10,000 packs, of which x will be packs with 20% players and y will be packs with 35% players.\r<BR>\n" );
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document.write( ".20x + .35y = 2600<BR>\n" );
document.write( "this tells you that when you add the number of star players from the 20% packs and the number of star players from the 35% packs, the total number of star players has to be 2600, because 2600 is 26% of 10,000.\r<BR>\n" );
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document.write( "the equations that need to be solved simultaneously are:\r<BR>\n" );
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document.write( "x + y = 10,000<BR>\n" );
document.write( ".20x + .35y = 2600\r<BR>\n" );
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document.write( "multiply the both sides of the second equation by 5 and leave the first equation as is to get:\r<BR>\n" );
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document.write( "x + y = 10,000<BR>\n" );
document.write( "x + 1.75y = 13,000\r<BR>\n" );
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document.write( "subtract the first equation from the second equation to get:<BR>\n" );
document.write( ".75y = 3,000<BR>\n" );
document.write( "divide both sides of that equation by .75 to get:<BR>\n" );
document.write( "y = 4000.<BR>\n" );
document.write( "since y = 4000, x has to be 6000, because x + y = 10,000.\r<BR>\n" );
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document.write( "you have x = 6000 and y = 4000.<BR>\n" );
document.write( "x + y = 10,000 is ok.<BR>\n" );
document.write( ".20x + .35y = .20*6000 + .35*4000 = 1200 + 1400 = 2600 is ok.\r<BR>\n" );
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document.write( "number of packs with 20% star players is 6000.<BR>\n" );
document.write( "number of packs with 35% star players is 4000.<BR>\n" );
document.write( "the total number of star players is .2*6000 + .35*4000 = 2600.<BR>\n" );
document.write( "2600 is 26% of 10,000.\r<BR>\n" );
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document.write( "everything looks good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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