document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476530>Question 476530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A shopper buys 3 oranges and 5 lemons for $10.26, while a second shopper buys 4 lemons and 6 oranges for $11.16. What is the price of each fruit?\r<BR>\n" );
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document.write( "I got 3x+5y=10.26 and 4x+6y=11.16\r<BR>\n" );
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document.write( "I gave the answer of  x=2.88   y=.324  but i was wrong. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326714 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=326714\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's a hint for future problems: use a letter for the variables that makes sense. In this problem instead of using x and y (easily confused) use O for oranges (that's letter O, not zero) and use L for lemons. Now write your equations.<BR>\n" );
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document.write( "For the three oranges and 5 lemons you get:<BR>\n" );
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document.write( "3*O + 5*L = 10.26<BR>\n" );
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document.write( "So far, no problem.<BR>\n" );
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document.write( "For the 4 lemons and 6 oranges you get:<BR>\n" );
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document.write( "6*O + 4*L = 11.16<BR>\n" );
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document.write( "Notice the difference in the second equation. You got the lemons and oranges reversed in order when you wrote 4x + 6y = 11.16.<BR>\n" );
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document.write( "Now you have the two equations:<BR>\n" );
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document.write( "3*O + 5*L = 10.26<BR>\n" );
document.write( "6*O + 4*L = 11.16<BR>\n" );
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document.write( "Multiply the top equation (both sides and all terms) by 2 to get:<BR>\n" );
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document.write( "6*O + 10*L = 20.52  <--- First equation doubled<BR>\n" );
document.write( "6*0 +  4*L = 11.16  <--- Second equation unchanged<BR>\n" );
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document.write( "Now subtract the two equations vertically and the answer becomes:<BR>\n" );
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document.write( "       6*L =  9.36<BR>\n" );
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document.write( "Solve for the price of lemons by dividing by 6 to get:<BR>\n" );
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document.write( "L = 1.56<BR>\n" );
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document.write( "Now let's return to the second equation and substitute 1.56 for L. This equation then becomes:<BR>\n" );
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document.write( "6*O + (4*1.56) = 11.16<BR>\n" );
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document.write( "Multiply the terms in the parentheses and the equation becomes:<BR>\n" );
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document.write( "6*O + 6.24 = 11.16<BR>\n" );
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document.write( "Subtract 6.24 from both sides and you have:<BR>\n" );
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document.write( "6*O = 4.92<BR>\n" );
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document.write( "Divide both sides by 6 to get:<BR>\n" );
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document.write( "O = 0.82<BR>\n" );
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document.write( "So oranges are 82 cents each and lemons are $1.56 each. <BR>\n" );
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document.write( "Hope this helped you out a little bit. You obviously know what you are doing, but just made a simple mistake.\r<BR>\n" );
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