A solution is to be kept between $86^{\circ}$ and $95^{\circ} \mathrm{F}$. What is the range of temperature in degree Celsius, if the Celsius (C)/ Fahrenheit (F) conversion formula is given by $F=\frac{9}{5} C+32$.
Suppose the temperature of the solution is $x$ degree Celsius.
$\therefore x$ in Fahrenheit $=\frac{9}{5} x+32$
Then, as per the given condition:
$86<\frac{9}{5} x+32<95$
$\Rightarrow 86-32<\frac{9}{5} x<95-32 \quad$ (Subtratcting 32 throughout)
$\Rightarrow 54<\frac{9}{5} x<63$
$\Rightarrow \frac{5}{9} \times 54<\frac{5}{9} \times \frac{9}{5} x<\frac{5}{9} \times 63 \quad$ (Multiplying by $\frac{5}{9}$ throughout)
$\Rightarrow 30 Hence, the range of the temperature in degree Celsius is between $30^{\circ} \mathrm{C}$ and $35^{\circ} \mathrm{C}$.