Question 100520
The answer to this question is -40 degrees. 
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The way to find this answer is to start with one of the versions of the equation for converting
between the temperature scales and make a substitution into it. For example, let's start with
the equation:
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{{{F = (9/5)C + 32}}}
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which is the form you normally use to find the Fahrenheit temperature if you know the Celsius
temperature.
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Now, since you want the temperature at which the Fahrenheit temperature (F) equals the Celsius 
temperature (C), you can substitute F for C in the equation because you have F = C. This
substitution changes the equation to:
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{{{F = (9/5)F + 32}}}
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You can get rid of the denominator on the right side by multiplying all the terms on
both sides of this equation by 5. When you do that multiplication the equation becomes:
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{{{5F = 9F + 160}}}
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Next get rid of the 9F on the right side by subtracting 9F from both sides to get:
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{{{-4F = 160}}}
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Solve this equation by dividing both sides by -4 which is the multiplier of F to get:
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{{{F = 160/(-4) = -40}}}
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And since we previously said that F equaled C, that means that when F is -40 degrees, 
C must also be -40 degrees.
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As practice exercises you could also start with the equation:
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{{{F = (9/5)C + 32}}}
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and substitute C for F and see if this doesn't also give you the answer that C = -40 degrees.
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Or you could start with the conversion equation:
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{{{C = (5/9)(F-32)}}}
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and try replacing C with F and solving. Then try replacing F with C and solving. In all
these you should get -40 degrees as the common answer.
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Therefore, you can say that at -40 degrees C the temperature is -40 degrees F.
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Hope this helps you to understand the problem.
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