Q.8. In countries like USA and Canada, 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

  1. Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.

  2. If the temperature is 30°C, what is the temperature in Fahrenheit?

  3. If the temperature is 95°F, what is the temperature in Celsius?

  4. 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?

  5. Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Solution:

(i) F = 95C + 32

The solutions can be tabulated as follows,

C

0

-10

F

32

14

Taking 1 unit = 10 on both x and y-axis

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(ii) Putting the value of C = 30 in F = 95 C+ 32 , we get,

F = 95×30 + 32 

= 54 + 32 = 86

(iii) Putting the value of F = 95 in F = 95 C+ 32 , we get,

95 = 95 C+ 32 

⇒C = (95 - 32)× 59

= 63 × 59

⇒ C = 35

(iv) Putting the value of F = 0 in F = 95 C+ 32 , we get

0 = 95 C+ 32 

⇒ C = - 32× 59

= 63 × 59

⇒ C = - 1609

Putting the value of C = 0 in F = 95 C+ 32 , we get,

F = 95 × 0 + 32 = 32

(v) Putting F = C in F = 95 C+ 32 , we get,

F = 95 F + 32

⇒ F - 95 F = 32

⇒ - 95 F = 32

⇒ F = - 40

Therefore both Fahrenheit and Celsius numerically the same at -40 oC = -40 oF.