Question

Calculate the temperature at which Fahrenheit and Celsius scales have the same reading.

Answer 1

Let the temperature be x

( x × 9/5 ) + 32 = x

9x / 5 + 32 = x

( 9x + 160 ) = 5x

9x - 5x = -160

4x = -160

x = -40

So, At -40° C the celsius and fahrenheit scales have the same reading. ( i.e., 40 )

Answer 2

Formula for Fahrenheit, F = 9/5 C + 32

Formula for Centigrade, C =5/9 (F-32)

Let F = C or C= F

F= C= 5/9(F-32)= (5F-160)/9

9F= 5F - 160

9F - 5F = -160

4F = -160

F = -160/4

F= -40 degree answer in Fahrenheit

C= F= 9/5 C + 32

C = (9C + 160)/5

5C = 9C + 160

5C - 9C = 160

-4C= 160

C=160/-4

C= -40 degree answer in Centigrade

Conclusion: The temperature wherein degrees centigrade is the same in degrees Fahrenheit is -40 degrees .