document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1066068>Question 1066068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Justin sells brownies for$2 each and cupcakes for $3 each. Justin sells a total of 100 brownies and cupcakes for $240. Write and solve a system of linear equations to find the number of brownies and the number of cupcakes Justin sold. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681245 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=681245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3>Let's set up the variables:<BR>\n" );
document.write( "b = number of brownies sold<BR>\n" );
document.write( "c = number of cupcakes sold\r<BR>\n" );
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document.write( "Justin sold 100 items (brownies and cupcakes only) so the two variables must add to 100<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc+=+100 ALIGN=MIDDLE  ALT=\"b%2Bc+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which we'll refer to as equation (1).\r<BR>\n" );
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document.write( "He sells brownies for $2 each. Which means that if he sells b brownies, then he collects 2*b dollars. In addition, he sells cupcakes for $3 each. Selling c cupcakes means he collects an additional 3*c dollars.\r<BR>\n" );
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document.write( "So far, the total is 2b+3c. This total must be $240 because this is the given total he collects. The second equation, labeled equation (2), is therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2B3c=240 ALIGN=MIDDLE  ALT=\"2b%2B3c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The system of equations is this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28b%2Bc+=+100%2C2b%2B3c=240%29 ALIGN=MIDDLE  ALT=\"system%28b%2Bc+=+100%2C2b%2B3c=240%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use that system to find the value of b and c.\r<BR>\n" );
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document.write( "Start with equation (1). Isolate b or c. Let's get b all by itself.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc+=+100 ALIGN=MIDDLE  ALT=\"b%2Bc+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc-c+=+100-c ALIGN=MIDDLE  ALT=\"b%2Bc-c+=+100-c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B0+=+100-c ALIGN=MIDDLE  ALT=\"b%2B0+=+100-c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+100-c ALIGN=MIDDLE  ALT=\"b+=+100-c\"   DISABLED_style= \"max-width:90%; height:auto;\" > Call this equation (3)\r<BR>\n" );
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document.write( "Notice how I just subtracted c from both sides.\r<BR>\n" );
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document.write( "Now move onto equation (2). Recall that equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2B3c=240 ALIGN=MIDDLE  ALT=\"2b%2B3c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What we'll do from here is replace 'b' with '100-c'. This works because of equation (3) above.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2B3c=240 ALIGN=MIDDLE  ALT=\"2b%2B3c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28b%29%2B3c=240 ALIGN=MIDDLE  ALT=\"2%28b%29%2B3c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28100-c%29%2B3c=240 ALIGN=MIDDLE  ALT=\"2%28100-c%29%2B3c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" > Notice how b is now gone after the substitution\r<BR>\n" );
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document.write( "Now solve for c\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28100-c%29%2B3c=240 ALIGN=MIDDLE  ALT=\"2%28100-c%29%2B3c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28100%29%2B2%28-c%29%2B3c=240 ALIGN=MIDDLE  ALT=\"2%28100%29%2B2%28-c%29%2B3c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200-2c%2B3c=240 ALIGN=MIDDLE  ALT=\"200-2c%2B3c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2B1c=240 ALIGN=MIDDLE  ALT=\"200%2B1c=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Bc=240 ALIGN=MIDDLE  ALT=\"200%2Bc=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B200=240 ALIGN=MIDDLE  ALT=\"c%2B200=240\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B200-200=240-200 ALIGN=MIDDLE  ALT=\"c%2B200-200=240-200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2B0=40 ALIGN=MIDDLE  ALT=\"c%2B0=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=40 ALIGN=MIDDLE  ALT=\"c=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Which means that Justin sold <font size=4 color=red>40 cupcakes</font>\r<BR>\n" );
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document.write( "Use the value of c to find b. We can use any equation with b & c in it. The easiest to use is equation (3).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+100-c ALIGN=MIDDLE  ALT=\"b+=+100-c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+100-40 ALIGN=MIDDLE  ALT=\"b+=+100-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > 'c' is replaced with 40 (since c = 40)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+60 ALIGN=MIDDLE  ALT=\"b+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <font size=4 color=red>60 brownies</font> were sold</font> </SPAN>\n" );
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