document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045376>Question 1045376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wholesaler is offering two different package deals of roses and carnations to florists. One package contains 20 dozen roses and 34 dozen carnations for $504.00. The other package contains 15 dozen roses and 17 dozen carnations for $327.00. Let x = cost of one dozen roses Let y = cost of one dozen carnations <BR>\n" );
document.write( "a. Write a system of equations for this problem. \r<BR>\n" );
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document.write( "b. Which equation can be multiplied by a coefficient to create an opposite coefficient? What is that value? \r<BR>\n" );
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document.write( "c. Solve this system for the cost of one dozen roses and the cost of one dozen carnations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660796 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=660796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = cost of one dozen roses.<BR>\n" );
document.write( "y = cost of one dozen carnations.\r<BR>\n" );
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document.write( "20x + 34y = 504<BR>\n" );
document.write( "15x + 17y = 327\r<BR>\n" );
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document.write( "you need to solve these 2 equations simultaneously.\r<BR>\n" );
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document.write( "if you multiply 17 by 2, you get 34.<BR>\n" );
document.write( "therefore, the coefficient of y is a good candidate.\r<BR>\n" );
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document.write( "multiply both sides of the second equation by 2 and leave the first equation as is to get:\r<BR>\n" );
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document.write( "20x + 34y = 504<BR>\n" );
document.write( "30x + 34y = 654\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "-10x = -150\r<BR>\n" );
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document.write( "solve for x to get x = 15.\r<BR>\n" );
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document.write( "replace x with 15 in either of the original equations and solve for y.\r<BR>\n" );
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document.write( "you will get y = 6\r<BR>\n" );
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document.write( "price of a dozen roses is 15 and price of a dozen carnations is 6.\r<BR>\n" );
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document.write( "note that i could also have done the following and gotten the same result.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "20x + 34y = 504<BR>\n" );
document.write( "15x + 17y = 327\r<BR>\n" );
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document.write( "multiply both sides of the second equation by -2 and leave the first equation as is to get:\r<BR>\n" );
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document.write( "20x + 34y = 504<BR>\n" );
document.write( "-30x - 34y = -654\r<BR>\n" );
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document.write( "add the 2 equations together to get:\r<BR>\n" );
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document.write( "-10x = -150\r<BR>\n" );
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document.write( "solve for x to get x = 150.\r<BR>\n" );
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document.write( "if i multiplied by plus 2, then i subtracted one equation from the other to eliminate the y variable.\r<BR>\n" );
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document.write( "if i multiplied by minus 2, then i added one equation to the other to eliminate the y variable.\r<BR>\n" );
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document.write( "both methods work.\r<BR>\n" );
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document.write( "choose the one you feel more comfortable with.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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