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If the temperature of a liquid can be measured in Kelvin units as $x^{\circ} K$ or in Fahrenheit units as $y^{\circ} F$, the relation between the two systems of measurement of temperature is given by the linear equation
$y=\frac{9}{5}(x-273)+32$
$(i)$ Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is $313^{\circ} K$.
$(ii)$ If the temperature is $158^{\circ} F$, then find the temperature in Kelvin.
Solution
$y=\frac{9}{5}(x-273)+32$
$(i)$ When the temperature of the liquid is $x=313^{\circ} K$
$y=\frac{9}{5}(313-273)+32=\frac{9}{5} \times 40+32=72^{0}+32^{0}=104^{\circ} F$
$(ii)$ When the temperature of the liquid is $y =158^{\circ} F$
$158=\frac{9}{5}(x-273)+32 \Rightarrow \frac{9}{5}(x-273)=158-32$
$\Rightarrow \quad x-273=126 \times \frac{5}{6}=70$
$\Rightarrow \quad x-273=70=273+70=343^{\circ} K$
