document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198352>Question 198352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you are shopping at the fruit market. You want to spend no more than $12.00 on apples and bananas. Bananas cost $2 per bunch, and apples cost $4 per bag. Find 3 possible combinations of bananas and apples that you can buy. Write each combination as an ordered pair. Let x be the number of banana bunches, and let y be the number of apple bags.\r<BR>\n" );
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document.write( "Please help me solve this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148864 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=148864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=# of banana bunches and y=# of apple bags\r<BR>\n" );
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document.write( "Since \"Bananas cost $2 per bunch, and apples cost $4 per bag\" and \"You want to spend no more than $12.00 on apples and bananas\", this means that we have the inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B4y%3C=12 ALIGN=MIDDLE  ALT=\"2x%2B4y%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B2y%29%3C=12 ALIGN=MIDDLE  ALT=\"2%28x%2B2y%29%3C=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF 2 on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y%3C=6 ALIGN=MIDDLE  ALT=\"x%2B2y%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=6-2y ALIGN=MIDDLE  ALT=\"x%3C=6-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2y from both sides.\r<BR>\n" );
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document.write( "Since \"x\" is the number of banana bunches, this means that \"x\" is a whole number that is NOT negative. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-2y%3E=0 ALIGN=MIDDLE  ALT=\"6-2y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > also.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-2y%3E=0 ALIGN=MIDDLE  ALT=\"6-2y%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%3E=2y ALIGN=MIDDLE  ALT=\"6%3E=2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2y to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%3C=6 ALIGN=MIDDLE  ALT=\"2y%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=3 ALIGN=MIDDLE  ALT=\"y%3C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2.\r<BR>\n" );
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document.write( "So you can buy at most 3 apple bags. Note: if you bought only apples, then you could only buy <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F4=3 ALIGN=MIDDLE  ALT=\"12%2F4=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > bags.\r<BR>\n" );
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document.write( "Since you can buy at most 3 apple bags, this means that the possible y values are: 0, 1, 2, and 3\r<BR>\n" );
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document.write( "Plug these values back into the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-2y ALIGN=MIDDLE  ALT=\"x=6-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-2%280%29 ALIGN=MIDDLE  ALT=\"x=6-2%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So one ordered pair is (6,0). In other words, in this case, you buy 6 banana bunches and no apple bags.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-2%281%29 ALIGN=MIDDLE  ALT=\"x=6-2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So one ordered pair is (4,1). In other words, in this case, you buy 4 banana bunches and 1 apple bag.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-2%282%29 ALIGN=MIDDLE  ALT=\"x=6-2%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So one ordered pair is (2,2). In other words, in this case, you buy 2 banana bunches and 2 apple bags.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-2%283%29 ALIGN=MIDDLE  ALT=\"x=6-2%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So one ordered pair is (3,0). In other words, in this case, you buy no banana bunches and 3 apple bags.\r<BR>\n" );
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document.write( "and so on...\r<BR>\n" );
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document.write( "Here are ALL the possible ordered pairs: (0,0), (0,1), (0,2), (0,3), (1,0), (1,1), (1,2), (2,0), (2,1), (2,2), (3,0), (3,1), (4,0), (4,1), (5,0), (6,0)\r<BR>\n" );
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document.write( "Take note that you are allowed to spend under $12. So the first ordered pair (0,0) means you did not buy anything.\r<BR>\n" );
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