document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350494>Question 350494</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The boiling and freezing temperatures of water are different in the two scales. Assuming that these scales are both linear – they really are, so that’s not an issue – is there any point at which the temperature in Fahrenheit would equal that in Celsius? What I mean is, suppose we took a piece of metal and heated – or cooled – it to a particular value on the one scale. Is there any such value for which a thermometer measuring the other scale would have the same number? What would that number be, and how did you find it?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250562 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=250562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I originally thought no, but then I thought about it again and came up with the fact that the degrees in Celsius will be equal to the degrees in Fahrenheit when the temperature is -40 degrees.\r<BR>\n" );
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document.write( "I figured if it had to happen, it would happen when the degrees were negative.\r<BR>\n" );
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document.write( "I traced the degrees in Celsius from 0 going down by 1 degree at a time and saw that the difference between Celsius and Fahrenheit was getting smaller as I went further down into the negative territory.\r<BR>\n" );
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document.write( "At -40 degrees, they were the same.\r<BR>\n" );
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document.write( "I then went back and figured out how I could do that using a formula.\r<BR>\n" );
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document.write( "This is what I found.\r<BR>\n" );
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document.write( "f = 1.8*c + 32\r<BR>\n" );
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document.write( "This means that the degrees in Fahrenheit is equal to the degrees in Celsius * 1.8 + 32.\r<BR>\n" );
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document.write( "You might be more familiar with f = 9/5 * c + 32.\r<BR>\n" );
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document.write( "Since 9/5 = 1.8, these formulas are the same.\r<BR>\n" );
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document.write( "The reverse formula is:\r<BR>\n" );
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document.write( "c = (f-32) / 1.8\r<BR>\n" );
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document.write( "this means that the degrees in Celsius equals the degrees in Fahrenheit minus 32 and then divided by 1.8.\r<BR>\n" );
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document.write( "If they are to be equal, then f must equal c.\r<BR>\n" );
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document.write( "f = c implies:\r<BR>\n" );
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document.write( "1.8*c + 32 = (f-32) / 1.8\r<BR>\n" );
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document.write( "Multiply both sides of that equation by 1.8 to get:\r<BR>\n" );
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document.write( "1.8 * (1.8*c + 32) = f - 32\r<BR>\n" );
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document.write( "Add 32 to both sides of that equation to ge t:\r<BR>\n" );
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document.write( "1.8 * (1.8*c + 32) + 32 = f\r<BR>\n" );
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document.write( "Since we know that f = 1.8*c + 32, then we can substitute in this equation to get:\r<BR>\n" );
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document.write( "1.8 * (1.8*c + 32) + 32 = 1.8*c + 32\r<BR>\n" );
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document.write( "Subtract 32 from both sides of this equation to get:\r<BR>\n" );
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document.write( "1.8 * (1.8*c + 32) = 1.8*c\r<BR>\n" );
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document.write( "Divide both sides of this equation by 1.8 to get:\r<BR>\n" );
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document.write( "1.8*c + 32 = c\r<BR>\n" );
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document.write( "Subtract 32 from both sides of this equation and subtract c from both sides of this equation to get:\r<BR>\n" );
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document.write( "1.8*c - c = -32\r<BR>\n" );
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document.write( "Combine like terms to get:\r<BR>\n" );
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document.write( ".8*c = -32\r<BR>\n" );
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document.write( "Divide both sides of this equation by .8 to get:\r<BR>\n" );
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document.write( "c = -32 / .8\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "c = -40.\r<BR>\n" );
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document.write( "The formula confirms the empirical results.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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