Question

Based on the values given above, which of the following mathematical relations between Fahrenheit and Celsius scale would be correct?​

Answer 1

Given :  values given  of Fahrenheit and Celsius  

To Find : mathematical relations between Fahrenheit and Celsius scale

Solution:

Fahrenheit Scale F     Celsius Scale C

    212°F                         100°C

    32°F                          0°C

   -40°F                         -40°C

C =aF  +  b

F = 32

C = 0

0 = a(32) + b

=> b = - 32a

C =aF  -32a

=> C = a(F - 32)

F = 212

C = 100

=> 100 = a(212 - 32)

=> 100 = a(180)

=>  5 = 9a

=> a = 5/9

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

=> C/5 = (F - 32)/9

C/5 = (F - 32)/9  this relation between Fahrenheit and Celsius scale would be correct

Verification  :

Fahrenheit Scale F     Celsius Scale C

      (F - 32)/9       =         C/5

    (212-32)/9 = 20    =   100/5 = 20

    (32-32)/9 =  0     =     0/5 =   0

    (-40-32)/9 = -8     =  -40/5 = -8

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