document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100352>Question 1100352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An average bagel contains 30 mg of calcium and 2 mg of iron. One ounce of cream cheese contains 25 mg of calcium and 0.4 mg of iron. If Leyla wants to eat a combination of bagels and cream cheese that contains exactly 370 mg of calcium and 12 mg of&#8203; iron, how much of each should she&#8203; eat?\r<BR>\n" );
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document.write( "How many bagels does she need to eat?\r<BR>\n" );
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document.write( "How many ounces of cream cheese does she need? </SPAN>\n" );
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document.write( "Let,<BR>\n" );
document.write( "x = number of bagels she needs to eat (this is a positive whole number)<BR>\n" );
document.write( "y = amount, in ounces, of cream cheese she needs to eat (this is some positive number which could be a whole number or a decimal number)\r<BR>\n" );
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document.write( "\"An average bagel contains 30 mg of calcium\" and \"One ounce of cream cheese contains 25 mg of calcium\". So if Leyla eats x bagels and y ounces of cream cheese, then she'll consume 30x+25y mg of calcium in total. She needs 370 mg of calcium meaning that the first equation is 30x+25y = 370\r<BR>\n" );
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document.write( "The second equation is 2x+0.4y = 12 because<BR>\n" );
document.write( "she gets 2 mg of iron from each bagel, so 2*x mg of iron from all the bagels she eats<BR>\n" );
document.write( "she also gets 0.4 mg of iron per ounce of cream cheese, giving another sub-total of 0.4*y mg of iron<BR>\n" );
document.write( "Overall she consumes 2x+0.4y mg of iron. This amount must be equal to 12 as this is the target value for iron.\r<BR>\n" );
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document.write( "The two equations in this system are<BR>\n" );
document.write( "30x+25y = 370<BR>\n" );
document.write( "2x+0.4y = 12\r<BR>\n" );
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document.write( "Let's solve the second equation for x<BR>\n" );
document.write( "2x+0.4y = 12<BR>\n" );
document.write( "2x+0.4y-0.4y = 12-0.4y <font color=blue>subtract 0.4y from both sides</font><BR>\n" );
document.write( "2x = 12-0.4y<BR>\n" );
document.write( "2x/2 = (12-0.4y)/2 <font color=blue>divide both sides by 2 to isolate x</font><BR>\n" );
document.write( "x = (12/2)-(0.4y/2)<BR>\n" );
document.write( "x = 6-0.2y\r<BR>\n" );
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document.write( "Then plug this into the first equation<BR>\n" );
document.write( "30x+25y = 370<BR>\n" );
document.write( "30*(x)+25y = 370<BR>\n" );
document.write( "30*(6-0.2y)+25y = 370 <font color=blue>x has been replaced with 6-0.2y</font>\r<BR>\n" );
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document.write( "Next we isolate y<BR>\n" );
document.write( "30*(6-0.2y)+25y = 370<BR>\n" );
document.write( "30*(6)+30*(-0.2y)+25y = 370 <font color=blue>distribute</font><BR>\n" );
document.write( "180-6y+25y = 370<BR>\n" );
document.write( "180+19y = 370<BR>\n" );
document.write( "180+19y-180 = 370-180 <font color=blue>subtract 180 from both sides</font><BR>\n" );
document.write( "19y = 190<BR>\n" );
document.write( "19y/19 = 190/19 <font color=blue>divide both sides by 19 to get y all by itself</font><BR>\n" );
document.write( "y = 10\r<BR>\n" );
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document.write( "Use this value of y to find x<BR>\n" );
document.write( "x = 6-0.2y<BR>\n" );
document.write( "x = 6-0.2*10 <font color=blue>replace y with 10</font><BR>\n" );
document.write( "x = 6-2<BR>\n" );
document.write( "x = 4\r<BR>\n" );
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document.write( "In summary we get<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "y = 10\r<BR>\n" );
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document.write( "Recall that at the top of the problem, we let,<BR>\n" );
document.write( "x = number of bagels she needs to eat <BR>\n" );
document.write( "y = amount, in ounces, of cream cheese she needs to eat\r<BR>\n" );
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document.write( "So Leyla needs to eat <font color=red>4 bagels</font> and <font color=red>10 ounces of cream cheese</font> to reach her goal (of consuming exactly 370 mg of calcium and 12 mg of iron)<BR>\n" );
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