document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200103>Question 1200103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts costs $15. If she bought a total of 7 shirts then how many of each kind did she buy </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834123 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = number of fancy shirts<BR>\n" );
document.write( "7-x = number of plain shirts\r<BR>\n" );
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document.write( "<tr><TD >Type</TD><TD >Number</TD><TD >Cost</TD></tr>\r\n" );
document.write( "<tr><TD >Fancy</TD><TD >x</TD><TD >28x</TD></tr>\r\n" );
document.write( "<tr><TD >Plain</TD><TD >7-x</TD><TD >15(7-x) = 105-15x</TD></tr>\r\n" );
document.write( "<tr><TD >Total</TD><TD >7</TD><TD >$131</TD></tr>\r\n" );
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document.write( "Total cost:<BR>\n" );
document.write( "fancy + plain = $131<BR>\n" );
document.write( "28x + (105-15x) = 131<BR>\n" );
document.write( "13x + 105 = 131<BR>\n" );
document.write( "13x = 131 - 105<BR>\n" );
document.write( "13x = 26<BR>\n" );
document.write( "x = 26/13<BR>\n" );
document.write( "x = 2\r<BR>\n" );
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document.write( "Fancy = x = 2<BR>\n" );
document.write( "Plain = 7-x = 7-2 = 5\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "1 fancy shirt = $28<BR>\n" );
document.write( "2 fancy shirts = 2*$28 = $56<BR>\n" );
document.write( "1 plain shirt = $15<BR>\n" );
document.write( "5 plain shirts = 5*$15 = $75<BR>\n" );
document.write( "2 fancy + 5 plain = $56 + $75 = $131 total<BR>\n" );
document.write( "2 fancy + 5 plain = 7 shirts total<BR>\n" );
document.write( "The answers are confirmed.\r<BR>\n" );
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document.write( "Another approach:\r<BR>\n" );
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document.write( "Let's say all 7 shirts were fancy.<BR>\n" );
document.write( "7*28 = 196<BR>\n" );
document.write( "She would spend $196\r<BR>\n" );
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document.write( "The gap from $131 to $196 is <BR>\n" );
document.write( "196-131 = 65<BR>\n" );
document.write( "Her total cost needs to drop by $65 to get to $131\r<BR>\n" );
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document.write( "Each time we subtract 1 fancy shirt, and add a plain shirt, we subtract a net cost of $13 (since -28+15 = -13)<BR>\n" );
document.write( "Then notice how 13 is a factor of 65<BR>\n" );
document.write( "65 = 13*5<BR>\n" );
document.write( "This tells us that we need to introduce 5 plain shirts\r<BR>\n" );
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document.write( "The 7 fancy shirts will drop to 7-5 = 2 fancy shirts.\r<BR>\n" );
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document.write( "Another approach:\r<BR>\n" );
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document.write( "x = number of fancy shirts<BR>\n" );
document.write( "y = number of plain shirts\r<BR>\n" );
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document.write( "x+y = 7 ... shirt count equation<BR>\n" );
document.write( "28x+15y = 131 .... shirt cost equation\r<BR>\n" );
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document.write( "Graph those two equations using something like Desmos or GeoGebra. Both are free.\r<BR>\n" );
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document.write( "The two equations intersect at (2,5)<BR>\n" );
document.write( "Meaning we have x = 2 fancy shirts and y = 5 plain shirts\r<BR>\n" );
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document.write( "x+y = 7 in green<BR>\n" );
document.write( "28x+15y = 131 in blue\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "<font color=red size=4>2 fancy and 5 plain</font><BR>\n" );
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