Question

The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = `(5F - 160)/9`. What is the numerical value of the temperature which is same in both the scales?

Answer 1

Given relation is, C = `(5F - 160)/9`  ......(i)

⇒ 9C = 5F – 160 

⇒ 5F = 9C + 160

⇒ F = `(9C + 160)/5`  .....(ii)

By given condition, C = F

Put this value in equation (i), we get

C = `(5C - 160)/9`

⇒ 9C = 5C – 160

⇒ 9C – 5C = – 160

⇒ 4C = – 160

⇒ C = (-160)/4`

⇒ C = – 40 = F  .....[Numerical value of the temperature]