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### Celsius and Fahrenheit Conversions

```
Date: 09/15/97 at 18:09:48
From: Anonymous
Subject: Fahrenheit and Celsius

Dr. Math:

I know that at -40 degrees Celsius and Fahrenheit the metric and
English temperatures are the same.  I am having problems with the
conversion method - I just don't understand.

My question is: For what value of C (if any) do both scales represent
temperature?

C = 5/9 (F-32)   or  F=9/5( F+32)  or  how do you set the two
different formulas up?

Thank you.

Kimberly
```

```
Date: 09/15/97 at 19:16:16
From: Doctor Anthony
Subject: Re: Fahrenheit and Celsius

Both scales represent temperature, and the formula

C
-------  = 5/9
F - 32

allows you to convert from one scale to the other.

Example. Convert a temperature of 180 degrees F to degrees C. This
means that the letter F in the formula is replaced by 180.

C
-------- = 5/9         C = (5/9) x 148   =  82.22 degrees C
180-32

Example(2). Convert 38 degrees C to degrees F. Now we replace the C in
the formula with 38 and find the value of F.

38        5
--------  = ----
F - 32      9

9 x 38 =  5(F-32)

342   =  5F - 160

502 =  5F

100.4 = F     so 38 degrees C is the same as  100.4 degrees F.

If you have a lot of conversions to make, it is sensible to draw a
graph with degrees C along the horizontal axis (say from 0 to 100
degrees) and degrees F up the vertical axis from 32 to 212. If you
plot the points (0,32) and (100,212) and join these points with a
straight line, then you can read from one scale to the other with the
minimum of effort.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 09/16/97 at 09:51:30
From: Anonymous
Subject: Re: Fahrenheit and Celsius

This is my question.... For what value of C (if any) do both scales
represent the temperature?

Thank you,

Kimberly
```

```
Date: 09/22/97 at 12:47:22
From: Doctor Rob
Subject: Re: Fahrenheit and Celsius

I think you are referring to the Fahrenheit and Celsius temperature
scales.

The relation is  F = 9*C/5 + 32, where F is the temperature in degrees
Fahrenheit, and C is the temperature in degrees Celsius. To find where
the number of degrees is the same on both scales, solve that equation
simultaneously with F = C.  This gives you two first-degree equations
in the two unknowns F and C.

Use one equation to solve for one of the variables. Substitute it into
the other equation. This will give you one first-degree equation in
the other unknown. Solve that for that unknown. Use its value to find
the first unknown using the formula you derived in the first step.

Hint:  Brrrrr!

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Temperature

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