document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119731>Question 119731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Body Temperature You may have heard that the average<BR>\n" );
document.write( "temperature of the human body is 98.6 degrees. Recent experiments<BR>\n" );
document.write( "show that the actual figure is closer to 98.2 degrees.† The<BR>\n" );
document.write( "figure of 98.6 comes from experiments done by Carl Wunderlich<BR>\n" );
document.write( "in 1868. But Wunderlich measured the temperatures<BR>\n" );
document.write( "in degrees Celsius and rounded the average to the<BR>\n" );
document.write( "nearest degree, giving 37 degree C as the average temperature.‡<BR>\n" );
document.write( "a. What is the Fahrenheit equivalent of 37 degree C?<BR>\n" );
document.write( "b. Given that Wunderlich rounded to the nearest degree<BR>\n" );
document.write( "Celsius, his experiments tell us that the actual average<BR>\n" );
document.write( "human body temperature is somewhere between 36.5 degree C<BR>\n" );
document.write( "and 37.5 degree C. Find what this range corresponds to in<BR>\n" );
document.write( "degrees Fahrenheit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87877 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=87877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "Body Temperature You may have heard that the average temperature of the human body is 98.6 degrees. <BR>\n" );
document.write( "Recent experiments show that the actual figure is closer to 98.2 degrees.† The<BR>\n" );
document.write( "figure of <BR>\n" );
document.write( "98.6 comes from experiments done by Carl Wunderlich in 1868. But Wunderlich measured the <BR>\n" );
document.write( "temperatures in degrees Celsius and rounded the average to the nearest degree, giving <BR>\n" );
document.write( "37 degree C as the average temperature.<BR>\n" );
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document.write( "Comment: this is some interesting historical information. It is background for the problem, but<BR>\n" );
document.write( "really doesn't affect the mechanics of the rest of the problem. Students that have trouble with <BR>\n" );
document.write( "\"word problems\" often have difficulty because they can't separate such \"extra\" information from<BR>\n" );
document.write( "what they are being asked to do for the problem. So you may want to read the above info for<BR>\n" );
document.write( "furthering your background knowledge of history and science, but you don't need it for solving<BR>\n" );
document.write( "this problem.<BR>\n" );
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document.write( "The heart of what this problem asks you to do is to convert some Celsius temperatures to<BR>\n" );
document.write( "Fahrenheit temperatures. The equation for doing such conversions is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+%289%2F5%29C+%2B+32 ALIGN=MIDDLE  ALT=\"F+=+%289%2F5%29C+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where F represents Fahrenheit degrees and C represents Celsius degrees.<BR>\n" );
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document.write( "Now that we have this information, let's work the two problems:<BR>\n" );
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document.write( "a. What is the Fahrenheit equivalent of 37 degree C?<BR>\n" );
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document.write( "All you have to do is to go to the conversion equation and in it substitute 37 for C. So start<BR>\n" );
document.write( "with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+%289%2F5%29C+%2B+32 ALIGN=MIDDLE  ALT=\"F+=+%289%2F5%29C+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Replace the C with 37 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+%289%2F5%2937+%2B+32 ALIGN=MIDDLE  ALT=\"F+=+%289%2F5%2937+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Determine the first term on the right side. You can do that by multiplying the 9 times the<BR>\n" );
document.write( "37 to get 333. Then divide the 333 by 5 to get 66.6. Substitute this for the first term<BR>\n" );
document.write( "on the right and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+66.6+%2B+32 ALIGN=MIDDLE  ALT=\"F+=+66.6+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now just add the two numbers on the right side and you get the sum as 98.6<BR>\n" );
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document.write( "So the answer to this first problem is that 37 degrees Celsius is equal to 98.6 degrees Fahrenheit.<BR>\n" );
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document.write( "Not too bad to do ...<BR>\n" );
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document.write( "Now for the second problem.<BR>\n" );
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document.write( "b. Given that Wunderlich rounded to the nearest degree Celsius, his experiments tell us that <BR>\n" );
document.write( "the actual average human body temperature is somewhere between 36.5 degree C<BR>\n" );
document.write( "and 37.5 degree C. <BR>\n" );
document.write( "Find what this range corresponds to in degrees Fahrenheit.<BR>\n" );
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document.write( "When you discard all the \"extra information\" in this problem, you are just being asked to <BR>\n" );
document.write( "find what the temperature range of 36.5 degrees C to 37.5 degrees C corresponds to in degrees F.<BR>\n" );
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document.write( "So let's return to the equation for converting degrees C to degrees F:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+%289%2F5%29C+%2B+32 ALIGN=MIDDLE  ALT=\"F+=+%289%2F5%29C+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And first substitute 36.5 for C in the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+%289%2F5%29%2836.5%29+%2B+32 ALIGN=MIDDLE  ALT=\"F+=+%289%2F5%29%2836.5%29+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can multiply the 9 times 36.5 to get 328.5 and then divide the 328.5 by the denominator 5<BR>\n" );
document.write( "and the answer becomes 65.7. Substitute this for the first term on the right side to reduce<BR>\n" );
document.write( "the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+65.7+%2B+32 ALIGN=MIDDLE  ALT=\"F+=+65.7+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And when you add the two numbers on the right side you get 97.7 degrees as the Fahrenheit<BR>\n" );
document.write( "equivalent of 36.5 degrees C.<BR>\n" );
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document.write( "Next you convert 37.5 degrees C to degrees F by using the same method:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+%289%2F5%29C+%2B+32+=+%289%2F5%29%2837.5%29+%2B+32+=+67.5+%2B+32+=+99.5 ALIGN=MIDDLE  ALT=\"F+=+%289%2F5%29C+%2B+32+=+%289%2F5%29%2837.5%29+%2B+32+=+67.5+%2B+32+=+99.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the Fahrenheit equivalent of 37.5 degrees C is 99.5 degrees F. <BR>\n" );
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document.write( "This tells us that the temperature range of 36.5 degrees C to 37.5 degrees C is (in Fahrenheit)<BR>\n" );
document.write( "97.7 degrees to 99.5 degrees.  <BR>\n" );
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document.write( "That's what the problem was really asking you to do.<BR>\n" );
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document.write( "Hope this helps you to see your way through it. Just remember the equation for converting<BR>\n" );
document.write( "Celsius temperatures to Fahrenheit is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+%289%2F5%29C+%2B+32 ALIGN=MIDDLE  ALT=\"F+=+%289%2F5%29C+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Just plug in Celsius <BR>\n" );
document.write( "temperatures for C, apply the algebra rules of multiplication, division, and addition, and<BR>\n" );
document.write( "the answer comes out in Fahrenheit.<BR>\n" );
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