document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=743755>Question 743755</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine how much of each food item you need in order to reach DV levels. Construct and solve a linear system of two equations that would make that determination. THE DV OF CALCIUM IS 1000 mg AND DV OF IRON IS 18 mg\r<BR>\n" );
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document.write( "The amount of calcium and iron (in milligrams) found in one 10 oz package of broccoli CALCIUM = 159 mg / IRON 2.04 mg\r<BR>\n" );
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document.write( "The amount of calcium and iron (in milligrams) found in a ½ cup of frozen corn<BR>\n" );
document.write( "CALCIUM = 9.09 mg /IRON = 0.95 mg\r<BR>\n" );
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document.write( "HOW DO I EVEN BEGIN TO WRITE THIS? LET ALONE SOLVE IT? THANK YOU FOR ANY HELP! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453043 by </B><A HREF=/tutors/aboutme.mpl?userid=davethejackal><B>davethejackal(28)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=davethejackal><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=davethejackal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=453043\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let c = half cups corn you eat.<BR>\n" );
document.write( "Let b = packets broccoli you eat\r<BR>\n" );
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document.write( "So if you are eating just corn and broccoli, the amount of calcium you will take in is:<BR>\n" );
document.write( "9.09 mg / half cup corn + 159  mp / pack broccoli)<BR>\n" );
document.write( "= 9.09c + 159b | [1]\r<BR>\n" );
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document.write( "The amount of calcium you need is 1000 mg<BR>\n" );
document.write( "So, using [1] we get 9.09c + 159b = 1000 | [3]\r<BR>\n" );
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document.write( "Similarly the amount of iron you get from eating the two foods is given by <BR>\n" );
document.write( "2.04 mg / pack broccoli + 0.95 / half cup of corn <BR>\n" );
document.write( "= 2.04b + 0.95c | [2]\r<BR>\n" );
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document.write( "The amount of iron we need is 18mg<BR>\n" );
document.write( "Hence from [2] we get 18 = 2.04b + 0.95c | [4]\r<BR>\n" );
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document.write( "Rearranging [3] gives <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+%281000+-+9.09c%29%2F159+ ALIGN=MIDDLE  ALT=\"+b+=+%281000+-+9.09c%29%2F159+\"   DISABLED_style= \"max-width:90%; height:auto;\" > | [5]\r<BR>\n" );
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document.write( "Substituting for b in [4] gives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.04%281000+-+9.09c%29%2F159+%2B0.95c+=+18+ ALIGN=MIDDLE  ALT=\"+2.04%281000+-+9.09c%29%2F159+%2B0.95c+=+18+\"   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=+2.04%281000%29%2F159+-+2.04%289.09c%29%2F159+%2B+0.95c+=+18+ ALIGN=MIDDLE  ALT=\"+2.04%281000%29%2F159+-+2.04%289.09c%29%2F159+%2B+0.95c+=+18+\"   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=+%280.95+-+2.04%289.09%29%2F159%29c+=+18+-+2.04%281000%29%2F159+ ALIGN=MIDDLE  ALT=\"+%280.95+-+2.04%289.09%29%2F159%29c+=+18+-+2.04%281000%29%2F159+\"   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=+c+=+%2818+-+2.04%2A%281000%29%2F159%29%2F%280.95+-+2.04%2A%289.09%29%2F159%29+ ALIGN=MIDDLE  ALT=\"+c+=+%2818+-+2.04%2A%281000%29%2F159%29%2F%280.95+-+2.04%2A%289.09%29%2F159%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence c= 6.20 half cups of corn (or 3.10 cups corn) to 2 dp\r<BR>\n" );
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document.write( "Substituting for c in [5] gives:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+%281000+-+9.09c%29%2F159+=+%281000-9.09%2A%286.20%29%29%2F159+ ALIGN=MIDDLE  ALT=\"+b+=+%281000+-+9.09c%29%2F159+=+%281000-9.09%2A%286.20%29%29%2F159+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "= 5.93 bags of broccoli.<BR>\n" );
document.write( "= 59.3 oz broccoli since there are 10 oz per bag.\r<BR>\n" );
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document.write( "Testing in original statements:\r<BR>\n" );
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document.write( "\" in one 10 oz package of broccoli CALCIUM = 159 mg / IRON 2.04 mg\"\r<BR>\n" );
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document.write( "Hence with 5.93 bags we have 159 x 5.93 g calcium = 942.87 g<BR>\n" );
document.write( "And 5.93 x 2.04 g iron = 12.10g (to 2 d.p.)\r<BR>\n" );
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document.write( "\"in a ½ cup of frozen corn CALCIUM = 9.09 mg /IRON = 0.95 mg \"\r<BR>\n" );
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document.write( "Hence in 6.2 half cups we get 9.09 x 6.2 g calcium = 56.36g (to 2 d.p)<BR>\n" );
document.write( "and we get 0.95 x 6.2 = 5.89g iron\r<BR>\n" );
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document.write( "Total amount of iron = 12.10+5.89 = 17.99 = 18.0 to 1 dp.<BR>\n" );
document.write( "Total amount of calcium = 942.87 + 56.36 = 999.23 QED (http://en.wikipedia.org/wiki/Q.E.D.)\r<BR>\n" );
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document.write( "That's a lot of broccoli! </SPAN>\n" );
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