36.5 Celsius Equals What in Fahrenheit

November 21, 2021

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Question 119731: Body Temperature You may have heard that the average
temperature of the human body is 98.6 degrees. Recent experiments
show that the actual figure is closer to 98.2 degrees.� The
figure of 98.6 comes from experiments done by Carl Wunderlich
in 1868. But Wunderlich measured the temperatures
in degrees Celsius and rounded the average to the
nearest degree, giving 37 degree C as the average temperature.�
a. What is the Fahrenheit equivalent of 37 degree C?
b. Given that Wunderlich rounded to the nearest degree
Celsius, his experiments tell us that the actual average
human body temperature is somewhere between 36.5 degree C
and 37.5 degree C. Find what this range corresponds to in
degrees Fahrenheit.
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Given:
.
Body Temperature You may have heard that the average temperature of the human body is 98.6 degrees.
Recent experiments show that the actual figure is closer to 98.2 degrees.� The
figure of
98.6 comes from experiments done by Carl Wunderlich in 1868. But Wunderlich measured the
temperatures in degrees Celsius and rounded the average to the nearest degree, giving
37 degree C as the average temperature.
.
Comment: this is some interesting historical information. It is background for the problem, but
really doesn't affect the mechanics of the rest of the problem. Students that have trouble with
"word problems" often have difficulty because they can't separate such "extra" information from
what they are being asked to do for the problem. So you may want to read the above info for
furthering your background knowledge of history and science, but you don't need it for solving
this problem.
.
The heart of what this problem asks you to do is to convert some Celsius temperatures to
Fahrenheit temperatures. The equation for doing such conversions is:
.

.
where F represents Fahrenheit degrees and C represents Celsius degrees.
.
Now that we have this information, let's work the two problems:
.
a. What is the Fahrenheit equivalent of 37 degree C?
.
All you have to do is to go to the conversion equation and in it substitute 37 for C. So start
with:
.

.
Replace the C with 37 to get:
.

.
Determine the first term on the right side. You can do that by multiplying the 9 times the
37 to get 333. Then divide the 333 by 5 to get 66.6. Substitute this for the first term
on the right and the equation becomes:
.

.
Now just add the two numbers on the right side and you get the sum as 98.6
.
So the answer to this first problem is that 37 degrees Celsius is equal to 98.6 degrees Fahrenheit.
.
Not too bad to do ...
.
Now for the second problem.
.
b. Given that Wunderlich rounded to the nearest degree Celsius, his experiments tell us that
the actual average human body temperature is somewhere between 36.5 degree C
and 37.5 degree C.
Find what this range corresponds to in degrees Fahrenheit.
.
When you discard all the "extra information" in this problem, you are just being asked to
find what the temperature range of 36.5 degrees C to 37.5 degrees C corresponds to in degrees F.
.
So let's return to the equation for converting degrees C to degrees F:
.

.
And first substitute 36.5 for C in the equation to get:
.

.
You can multiply the 9 times 36.5 to get 328.5 and then divide the 328.5 by the denominator 5
and the answer becomes 65.7. Substitute this for the first term on the right side to reduce
the equation to:
.

.
And when you add the two numbers on the right side you get 97.7 degrees as the Fahrenheit
equivalent of 36.5 degrees C.
.
Next you convert 37.5 degrees C to degrees F by using the same method:
.

.
So the Fahrenheit equivalent of 37.5 degrees C is 99.5 degrees F.
.
This tells us that the temperature range of 36.5 degrees C to 37.5 degrees C is (in Fahrenheit)
97.7 degrees to 99.5 degrees.
.
That's what the problem was really asking you to do.
.
Hope this helps you to see your way through it. Just remember the equation for converting
Celsius temperatures to Fahrenheit is: . Just plug in Celsius
temperatures for C, apply the algebra rules of multiplication, division, and addition, and
the answer comes out in Fahrenheit.
.