document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114129>Question 114129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A football team is planning a banquet.  It offers 2 types of meals.  The first one is a turkey plate for $8.00 the second is a roast beef plate for $12.00.  The total budget is $980.00 for 100 people.  X is the turkey and Y is the roast.<BR>\n" );
document.write( "X + Y = 100<BR>\n" );
document.write( "8<BR>\n" );
document.write( "X +12Y =980<BR>\n" );
document.write( "a) solve the system of equations by elimination.<BR>\n" );
document.write( "b) How many turkey plates are sold?<BR>\n" );
document.write( "c) How many roast beef plates are sold? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83061 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=83061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "X + Y = 100<BR>\n" );
document.write( "8X +12Y =980<BR>\n" );
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document.write( "To solve these two equations by elimination, either the terms in the X column or the terms<BR>\n" );
document.write( "in the Y column must be equal in size. Let's make the terms in the X column equal. We can<BR>\n" );
document.write( "do that by multiplying the top equation (all terms on both sides) by 8. When we do that multiplication<BR>\n" );
document.write( "the two equations are:<BR>\n" );
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document.write( "8X + 8Y = 800<BR>\n" );
document.write( "8X +12Y = 980<BR>\n" );
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document.write( "Now if we subtract vertically in the columns the 8X from the bottom equation is subtracted<BR>\n" );
document.write( "from the 8X in the top equation ... leaving 0X which means the X variable is now gone.<BR>\n" );
document.write( "The 12Y from the bottom equation is taken from the 8Y in the top equation leaving<BR>\n" );
document.write( "-4Y. And on the other side of the equation the 980 from the bottom equation is subtracted<BR>\n" );
document.write( "from the 800 in the top equation resulting in -180. So after vertically subtracting<BR>\n" );
document.write( "the two equations we are left with the equation:<BR>\n" );
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document.write( "-4Y = -180<BR>\n" );
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document.write( "Dividing both sides of this equation by -4 (which is the multiplier of the Y), we have:<BR>\n" );
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document.write( "Y = -180/-4 = 180/4 = 45<BR>\n" );
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document.write( "So 45 roast beef plates are sold. [This is the answer to part c.]<BR>\n" );
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document.write( "But a total of 100 plates were sold. So the remaining 55 plates have to be the number<BR>\n" );
document.write( "of turkey plates sold. [This is the answer to part b.]<BR>\n" );
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document.write( "We could also have solved this problem by eliminating the Y column of the two equations.<BR>\n" );
document.write( "Starting with the two original equations:<BR>\n" );
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document.write( "X + Y = 100<BR>\n" );
document.write( "8X +12Y =980<BR>\n" );
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document.write( "we could have multiplied all terms of the top equation by 12 to make the equations<BR>\n" );
document.write( "become:<BR>\n" );
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document.write( "12X +12Y =1200<BR>\n" );
document.write( "8X + 12Y = 980<BR>\n" );
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document.write( "When you subtract these two equations vertically, the Y terms cancel out and the resulting <BR>\n" );
document.write( "equation is:<BR>\n" );
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document.write( "4X  = 220<BR>\n" );
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document.write( "Dividing both sides by 4 results in:<BR>\n" );
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document.write( "X = 220/4 = 55<BR>\n" );
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document.write( "Again we have found that X, the number of turkey plates, is 55, but this time we found the<BR>\n" );
document.write( "answer to part b of the problem first ... in the order asked for by the problem.<BR>\n" );
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document.write( "The answer to part c, the number of roast beef plates sold, is then found by subtracting<BR>\n" );
document.write( "the number of turkey plates (55) from 100 (total plates sold) to again get 45 as the answer.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to solve it by elimination.<BR>\n" );
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document.write( " </SPAN>\n" );
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