The Celsius and Fahrenheit Scales

Question

At what temperature is the Fahrenheit scale reading equal to (a) twice that of the Celsius scale and (b) half that of the Celsius scale?

kuma · Answer

Fahrenheit = Celsius * 1.800 + 32
 
Fahrenheit is twice that of Celsius, so 2 Fahrenheit = 1 Celsius
Lets make the temperature we are solving for "X" (which will be the temperature in celclius)
 
 
2X = 1.800X + 32 
Lets get X on one side of the equation but subtracting 2X from both sides
 
2X - 2X = 1.800X + 32 - 2X
0 = 1.800X + 32 - 2X
Now, we can further isolate X but subtracting 32 from each side
 
0 - 32 = 1.800*X + 32 - 32 - 2X
-32 = 1.800X - 2X
Now, combine like terms (1.800X and 2X are both a number * X)
 
-32 = -.2X
Multiply each side by -1 to get rid of the negative sign so
 
32 = .2X
Solve for X by dividing each side by .2
32/.2 = .2X/.2
 
X=160C. 
This is your temperature in celsius. You can double it to get your temperature in F.
160*2 = 320F.
 
Answer for (a), 320F, 160C
 
Using similar logic, lets make it X/2 this time (because Fahrenheight is half that of Celsius).
 
X/2 = 1.800(X) + 32 
Isolate X like last time to get
 
0 = 1.800(X) + 32 - (X/2)
Keep isolating by subtracting that 32.. :)
 
-32 = 1.800(X) - (X/2)
Same idea as last time, lets combine like terms! X/2 can be rewritten .5X which will make things easier
 
-32 = 1.800(X) - .5X
This makes it easier to do the math! You are simply subtracting 1.800-.5 (which equals 1.3)
 
-32 = 1.3X
Now divide each side by 1.3
 
-32 / 1.3 = 1.3X / 1.3
-24.615 = X
 
This is your answer for C. Divide it by 2 to get F.
 
-24.615/2 = 12.31
 
Answer for (b), -12.3F, -24.6C

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The Celsius and Fahrenheit Scales

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