document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116746>Question 116746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many pounds of hamburger that costs $1.10 per pound must be mixed with 50 pounds of hamburger that costs $1.80 per pound to make a mixure that costs $1.30 per pound. \r<BR>\n" );
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document.write( "I can get the answer by working it out but can't get the correct equation down on paper.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84883 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=84883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the unknown number of pounds of meat at $1.10 per pound that will be added to the <BR>\n" );
document.write( "mix. <BR>\n" );
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document.write( "The net worth of this meat will be the cost per pound times the number of pounds to be added.<BR>\n" );
document.write( "So the total cost of this meat will be 1.10*x.<BR>\n" );
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document.write( "For the other meat in the mix you have 50 pounds and it is priced at $1.80 per pound. So<BR>\n" );
document.write( "this meat is worth 50 pounds times $1.80 per pound or 90 dollars.<BR>\n" );
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document.write( "The total amount of meat in the mix will be the total of x pounds plus 50 pounds ... an amount<BR>\n" );
document.write( "equal to (50 + x) pounds. Since this meat is to be worth $1.30 per pound, the dollar amount<BR>\n" );
document.write( "of the mixed meat will be its weight (50 + x pounds) times $1.30 per pound.<BR>\n" );
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document.write( "Now we can write a cash based equation. The dollar amount of the $1.10 meat plus the dollar<BR>\n" );
document.write( "amount of the $1.80 meat must equal the dollar amount of the mixed meat. In equation form<BR>\n" );
document.write( "this is:<BR>\n" );
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document.write( "1.10*x + 50*1.80 = (50 + x)* 1.30<BR>\n" );
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document.write( "Multiplying 50*1.8 gives 90 and this makes the equation become:<BR>\n" );
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document.write( "1.10x + 90 = (50 + x)*1.30<BR>\n" );
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document.write( "Doing the distributed multiplication on the right side makes the equation:<BR>\n" );
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document.write( "1.10x + 90 = 50*1.30 + 1.30x<BR>\n" );
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document.write( "and 50 times 1.30 equals 65 which makes the equation:<BR>\n" );
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document.write( "1.10x + 90 = 65 + 1.30x<BR>\n" );
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document.write( "Get rid of the 90 on the left side by subtracting 90 from both sides:<BR>\n" );
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document.write( "1.10x = -25 +1.30x<BR>\n" );
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document.write( "Get rid of the 1.30x on the right side by subtracting 1.30x from both sides:<BR>\n" );
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document.write( "-0.2x = -25<BR>\n" );
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document.write( "Solve for x by dividing both sides by -0.2 and you get:<BR>\n" );
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document.write( "x = 125<BR>\n" );
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document.write( "This tells you that you add 125 pounds of meat that costs $1.10 per pound to 50 pounds of<BR>\n" );
document.write( "meat that costs $1.80 per pound and you get 175 pounds (50 + 125) of meat that is worth $1.30<BR>\n" );
document.write( "per pound. <BR>\n" );
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document.write( "Check: 125 pounds of meat at $1.10 per pound is 125*1.10 = $137.50. And 50 pounds of meat<BR>\n" );
document.write( "at $1.80 per pound is the $90 that we previously found. So the two groups of meat are worth<BR>\n" );
document.write( "a total of $137.50 + $90.00 = $227.50.<BR>\n" );
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document.write( "This makes 175 pounds of meat that is intended to be sold for $1.30 per pound. 175 times 1.30 = $227.50<BR>\n" );
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document.write( "So the mixed meat is worth the same as the sum of the two individual amounts of meat ... the <BR>\n" );
document.write( "answer checks. And the answer is 125 pounds of meat worth $1.10 per pound.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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