If the temperature of a liquid can be measured in Kelvin units as $x$ K and in Fahrenheit units as $y$ °F, the relation between the two systems of measurement of temperature is given by the linear equation $$y = \left(\frac{9}{5}\right)(x - 273) + 32$$

(A) Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313 K.

(B) If the temperature is 158 °F, then find the temperature in Kelvin.

(A) $x = 313 K$

$$y = \left(\frac{9}{5}\right)(313 - 273) + 32$$

$$= \left(\frac{9}{5}\right)(40) + 32$$

$$= 72 + 32 = 104 \text{ °F}$$

(B) $y = 158$ °F;

$$158 = \left(\frac{9}{5}\right)(x - 273) + 32$$

$$\Rightarrow 126 = \left(\frac{9}{5}\right)(x - 273)$$

$$\Rightarrow x - 273 = 126 \times \left(\frac{5}{9}\right) = 70$$

$$\Rightarrow x = 343 \text{ K}$$