document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=245386>Question 245386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help please.\r<BR>\n" );
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document.write( "Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for both variables.\r<BR>\n" );
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document.write( "1.The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What are the length and the width? \r<BR>\n" );
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document.write( "2. 30,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $201,000. How many people paid $13.00 for reserved seats, and how many paid $4.00 for general admission? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179254 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.<BR>\n" );
document.write( "1.The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What are the length and the width?<BR>\n" );
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document.write( "L=original length, W=original width<BR>\n" );
document.write( "The perimeter of a rectangle is six times the width.<BR>\n" );
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document.write( "perimeter:  <BR>\n" );
document.write( "2L + 2W = 6W<BR>\n" );
document.write( "2L = 6W - 2W<BR>\n" );
document.write( "2L = 4W<BR>\n" );
document.write( "Simplify, divide both sides by 2<BR>\n" );
document.write( "L = 2W<BR>\n" );
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document.write( "If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches.<BR>\n" );
document.write( "2(L+4) + 2(W+7) = 160<BR>\n" );
document.write( "2L + 8 + 2W + 14 = 160<BR>\n" );
document.write( "2L + 2W + 22 = 160<BR>\n" );
document.write( "2L + 2W = 160 - 22<BR>\n" );
document.write( "2L + 2W = 138<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "L + W = 69<BR>\n" );
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document.write( " What are the length and the width?<BR>\n" );
document.write( "From the 1st statement we know L=2W; replace L with 2W<BR>\n" );
document.write( "2W + W = 69<BR>\n" );
document.write( "3W = 69<BR>\n" );
document.write( "W = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69%2F3 ALIGN=MIDDLE  ALT=\"69%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "W = 23 is the width<BR>\n" );
document.write( "then<BR>\n" );
document.write( "L = 2(23)<BR>\n" );
document.write( "L = 46 is the width<BR>\n" );
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document.write( "Check solution in the 1st statement:<BR>\n" );
document.write( "\"The perimeter of a rectangle is six times the width.\"<BR>\n" );
document.write( "2(46) + 2(23) = 6(23)<BR>\n" );
document.write( "92 + 46 = 138;<BR>\n" );
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document.write( "YOu can check the solution using the 2nd statement<BR>\n" );
document.write( "\"If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. \"<BR>\n" );
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document.write( "2. 30,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $201,000. How many people paid $13.00 for reserved seats, and how many paid $4.00 for general admission?<BR>\n" );
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document.write( "Let g = no. of general admission tickets<BR>\n" );
document.write( "Let r = no. of reserved<BR>\n" );
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document.write( "Total attendance equation<BR>\n" );
document.write( "g + r = 30000<BR>\n" );
document.write( "or<BR>\n" );
document.write( "g = (30000-r)<BR>\n" );
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document.write( "Total receipts equation<BR>\n" );
document.write( "4g + 13r = 201000<BR>\n" );
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document.write( "Substitute (30000-r) for g in the above equation<BR>\n" );
document.write( "4(30000-r) + 13r = 201000<BR>\n" );
document.write( "120000 - 4r + 13r = 201000<BR>\n" );
document.write( "9r = 201000 - 120000<BR>\n" );
document.write( "9r = 81000<BR>\n" );
document.write( "fr = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81000%2F9 ALIGN=MIDDLE  ALT=\"81000%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r = 9000 reserved tickets sold<BR>\n" );
document.write( "and<BR>\n" );
document.write( "30000 - 9000 = 21000 general admission tickets<BR>\n" );
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document.write( "Check solution using the receipt equation<BR>\n" );
document.write( "4(21000) + 13(9000) = <BR>\n" );
document.write( "84000 + 117000 = 201000<BR>\n" );
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