document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179258>Question 1179258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On<BR>\n" );
document.write( " the first day, Cindy sells 6 adult tickets and 5 children's tickets for a total of 112.50. on the second day, she sells 8 adult tickets and 4 children's tickets for a total of 130.00 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808781 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=808781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The first tutor always solves systems of equations using substitution.  That might be her preferred method; but when both equations are given in Ax+By=C form, I think some sort of elimination is much easier.<br><BR>\n" );
document.write( "Below is an unusual method for solving the problem.  I first present the solution informally using logical reasoning; then I show the corresponding formal algebraic solution.  The method shown can make the solution of some similar problems easier than standard elimination; but for most problems a more straightforward solution using elimination will be fastest.<br><BR>\n" );
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document.write( "\"On the first day, Cindy sells 6 adult tickets and 5 children's tickets for a total of 112.50.\"<BR>\n" );
document.write( "\"On the second day, she sells 8 adult tickets and 4 children's tickets for a total of 130.00\"<br><BR>\n" );
document.write( "The difference between the two sales is 2 more adult tickets and 1 fewer children's tickets for $17.50 more.<br><BR>\n" );
document.write( "Apply that difference four more times to make the number of children's tickets zero.  Doing that gives us 8+4(2) = 16 adult tickets and 4-4(1) =  0 children's tickets for a total of $130+4($17.50)=$200.<br><BR>\n" );
document.write( "So the cost of each adult ticket is $200/16 = $12.50.<br><BR>\n" );
document.write( "Then use the purchase on the second day to determine the cost of each children's ticket:<BR>\n" );
document.write( "8($12.50)+4x = $130<BR>\n" );
document.write( "4x = $30<BR>\n" );
document.write( "x = $30/4 = $7.50<br><BR>\n" );
document.write( "ANSWER: Adult ticket price $12.50; Children's ticket price $7.50<br><BR>\n" );
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document.write( "Algebraically, this unusual solution method looks like this:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%286a%2B5c=112.5%2C8a%2B4c=130%29 ALIGN=MIDDLE  ALT=\"system%286a%2B5c=112.5%2C8a%2B4c=130%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Find the difference between the two equations:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a-c+=+17.50%7D%7D%3Cbr%3E%0D%0ANow+use+this+system%3A%3Cbr%3E%0D%0A%7B%7B%7Bsystem%288a%2B4c=130%2C2a-c=17.50%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply the second equation by 4:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%288a%2B4c=130%2C8a-4c=70%29 ALIGN=MIDDLE  ALT=\"system%288a%2B4c=130%2C8a-4c=70%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Add the two equations to eliminate c:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16a=200 ALIGN=MIDDLE  ALT=\"16a=200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+200%2F16+=+12.50 ALIGN=MIDDLE  ALT=\"a+=+200%2F16+=+12.50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use that value for a to find c:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2812.50%29%2B4c+=+130 ALIGN=MIDDLE  ALT=\"8%2812.50%29%2B4c+=+130\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4c+=+30 ALIGN=MIDDLE  ALT=\"4c+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+7.50 ALIGN=MIDDLE  ALT=\"c+=+7.50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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document.write( "So why use this unusual method for solving the problem?<br><BR>\n" );
document.write( "In a formal algebraic solution, finding the difference between the two original equations gives us an equation in which one of the coefficients is -1.  That will make solving the system by elimination easier, because it will keep the coefficients smaller.<br><BR>\n" );
document.write( "And if a formal algebraic solution is not required, this method of solving the problem makes an informal solution easier, for the same reason.<br><BR>\n" );
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