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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 30C, what is the temperature in Fahrenheit?
(iii) If the temperature is 95F, what is the temperature in Celsius?
(iv) If the temperature is 0C, what is the temperature in Fahrenheit and if the temperature is 0F, 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=9532
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
F95F=32
5F9F5=32
45F=32
F=32×54
F=40
Therefore at 40, both Fahrenheit and Celsius are numerically the same.

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