  Question

# Question 8 In countries like USA and Canada, the temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius. Here is a linear equation that converts Fahrenheit to Celsius:                                            F=95C+32 (i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for the y-axis. (ii) If the temperature is 30∘C, what is the temperature in Fahrenheit? (iii) If the temperature is 95∘F, what is the temperature in Celsius? (iv) If the temperature is 0∘C, what is the temperature in Fahrenheit and if the temperature is 0∘F, what is the temperature in Celsius? (v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Solution

## (i)F=95C+32 When C=0 then F=32 also, when C=5 then F=41 C05F3241 (ii) Putting the value of C=30 in F=95C+32, we get F=95×30+32 ⇒F=54+32 ⇒F=86 (iii) Putting the value of F=95 in F=95C+32, we get 95=95C+32 ⇒95C=95−32 ⇒C=63×59 ⇒C=35 (iv) Putting the value of F=0 in F=95C+32, we get 0=95C+32 ⇒95C=−32 ⇒C=−32×59 ⇒C=−1609 Putting the value of C=0 in F=95C+32, we get F=95×0+32 ⇒F=32 (v) Here, we have to find when F=C. Therefore, Putting F=C in F=95C+32, we get F=95F+32 ⇒F−95F=32 ⇒5F−9F5=32 ⇒−45F=32 ⇒F=32×5−4 ⇒F=−40 Therefore at −40, both Fahrenheit and Celsius are numerically the same.  Suggest corrections   