document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126089>Question 1126089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Protein(grams/serving) macaroni 3 broccoli 2<BR>\n" );
document.write( "Carbohydrates (grams/serving) macaroni 16 broccoli 4<BR>\n" );
document.write( "How many servings of each would it take to get exactly 37 grams of protein and 164 grams of carbohydrates?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742449 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=742449\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of servings of macaroni and y = the number of servings of broccoli.\r<BR>\n" );
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document.write( "macaroni has 3 grams of protein per serving and 2 gram of carbohydrates per serving.\r<BR>\n" );
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document.write( "macaroni has 16 grams of carbohydrates per serving and broccoli has 4 grams of carbohydrates per serving.\r<BR>\n" );
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document.write( "if you want a total of 37 grams of protetin and 164 grams of carbohydrates, ten your equations are:\r<BR>\n" );
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document.write( "3x + 2y = 37<BR>\n" );
document.write( "16x + 4y = 164\r<BR>\n" );
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document.write( "the first equation says 3 grams of protein per serving times the number of servings of macaroni plus 2 grams of protein per serving times the number of servings of broccoli equals a total of 37  grams of protein.<BR>\n" );
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document.write( "the second equation says 16 grams of carbohydrates per serving times the number of servings of macaroni plus 4 grams of carbohydrates per serving times the number of servings of broccoli equals a total of 164 grams of carbohydrates.\r<BR>\n" );
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document.write( "you need to solve these equations simultaneously so the same number of servings of macaroni and broccoli apply to both equations.\r<BR>\n" );
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document.write( "if you graphed these equations, your solution would be the intersection of the graphs of both equations, as shown below:\r<BR>\n" );
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document.write( "from the graph, you can see that the intersection of the two lines is the point (9,5).\r<BR>\n" );
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document.write( "that means the value of x = 9 and y = 5.\r<BR>\n" );
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document.write( "that means 9 servings of macaroni and 5 servings of broccoli is the solution.\r<BR>\n" );
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document.write( "3 * 9 + 2 * 5 = 27 + 10 = 37 grams of protein.\r<BR>\n" );
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document.write( "16 * 9 + 4 * 5 = 144 + 20 = 164 grams of carbohydrates.\r<BR>\n" );
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document.write( "the solution looks good.\r<BR>\n" );
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document.write( "to solve this problem algebraically, you would do the following:\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "3x + 2y = 37<BR>\n" );
document.write( "16x + 4y = 164\r<BR>\n" );
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document.write( "multiply the first equation by 2 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "6x + 4y = 74<BR>\n" );
document.write( "16x + 4y = 164\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "10x = 90\r<BR>\n" );
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document.write( "divide both sides of this equation by 10 t9o get x = 9.\r<BR>\n" );
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document.write( "replace x with 9 in either original equaiton (i used the first), to get:\r<BR>\n" );
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document.write( "3*9 + 2y = 37 which becomes 27 + 2y = 37.<BR>\n" );
document.write( "subtract 27 from both sides to get 2y = 10<BR>\n" );
document.write( "solve for y to get y = 5.\r<BR>\n" );
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document.write( "your solution is x = 9 and y = 5.<BR>\n" );
document.write( "since this agrees with the graphical solution, there is no need for further confirmation that the solution is valid.\r<BR>\n" );
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document.write( "your solution is you need 9 servings of macaroni and 5 servings of broccoli.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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