Question

In an experiment, a solution of hydrochloric acid is to be kept between ${30}^{\circ }$ and ${35}^{\circ }$ Celsius. What is the range of temperature in degree Fahrenheit if conversion formula is given by $C=\frac{5}{9}(F-32),$ where $C$ and $F$ represent temperature in degree celsius and degree Fahrenheit, respectively.

Answer 1

Given: $C=\frac{5}{9}(F-32)$

Given: The solution is to be kept between ${30}^{\circ }C$ and ${35}^{\circ }C$

i.e., ${30}^{\circ }<C<{35}^{\circ }$

$\Rightarrow 30<\frac{5}{9}(F-35)<{35}^{\circ }$

Multiplying $\frac{9}{5}$ on all sides.

$\Rightarrow 30\times \frac{9}{5}<\frac{9}{5}\times \frac{5}{9}(F-32)<35\times \frac{9}{5}$

$\Rightarrow 9\times 6<F-32<7\times 9$

$\Rightarrow 54<F-32<63$

$\Rightarrow 54<F-32<63$

Adding $32$ on all sides
$\Rightarrow 54+32<F-32+32<63+32$

$\Rightarrow 86<F<95$

$\therefore$ The required range of temperature is between ${86}^{\circ }F$ and ${95}^{\circ }F$.