Question

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:
$F=\left(\frac{9}{5}\right)C+32$
(i) Draw the graph of the linear equation above using Celsius for $x$-axis and Fahrenheit for $y$-axis.
(ii) If the temperature is ${30}^{o}C$, what is the temperature in Fahrenheit?
(iii) If the temperature is ${95}^{o}F$, what is the temperature in Celsius?
(iv) If the temperature is $0^{o}C$, what is the temperature in Fahrenheit and if the temperature is $0^{o}F$, 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.

Answer 1

(i) Since the equation between $F$ and $C$ is given, the graph can be drawn as shown above.

(ii) Given $c=30$, so $F=\frac{9}{5}\times 30+32=86F$.

(iii) Given $F=95$, so $C=\frac{5}{9}\times (F-32)=35C$.

(iv) Given $C=0$, so $F=32$ and if $F=0$, we get $C=-\frac{160}{9}$.

(v) Put $F=C=x$ in given equatin, we get $\frac{4x}{5}=-32$, from which we get $x=-40$

Yes, there is a temperature which is numerically the same in both fahrenheit and celsius, the numerical value is $-40$.