Question

A solution is to be kept between ${68}^{\circ }F$ and ${77}^{\circ }F$. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by $F=\frac{9}{5}C+32$ $?$

Answer 1

Simplification
Given that: $F=\frac{9}{5}C+32$
And the solution is to be kept between ${68}^{\circ }F$ and ${77}^{\circ }F$,
Hence $68<F<77$
$\Rightarrow 68<\frac{9}{5}C+32<77$
Subtracting $32$ from all sides
$\Rightarrow 68-32<\frac{9}{5}C+32-32<77-32$
$\Rightarrow 36<\frac{9}{5}C<45$
Multiplying with $\frac{5}{9}$ on all sides.
$\Rightarrow 36\times \frac{5}{9}<\frac{9}{5}C\times \frac{5}{9}<45\times \frac{5}{9}$
$\Rightarrow 20<C<25$
$\therefore$ The value of ${}^{\circ }C$ is between ${20}^{\circ }C$ and ${25}^{\circ }C$.