Question:
A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by
$\mathrm{F}=\frac{9}{8} \mathrm{C}+32 ?$
Solution:
Since the solution is to be kept between $68^{\circ} \mathrm{F}$ and $77^{\circ} \mathrm{F}$,
$68 Putting $\mathrm{F}=\frac{9}{5} \mathrm{C}+32$, we obtain $68<\frac{9}{5} \mathrm{C}+32<77$ $\Rightarrow 68-32<\frac{9}{5} \mathrm{C}<77-32$ $\Rightarrow 36<\frac{9}{5} \mathrm{C}<45$ $\Rightarrow 36 \times \frac{5}{9}<\mathrm{C}<45 \times \frac{5}{9}$ $\Rightarrow 20<\mathrm{C}<25$ Thus, the required range of temperature in degree Celsius is between 20°C and 25°C.