Question

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

Answer 1

It is given that ${68}^{\circ }<F<{77}^{\circ }$

Putting $F=\frac{9}{5}C+32$, we have

${68}^{\circ }<\frac{9}{5}C+32<{77}^{\circ }$

$\Rightarrow {36}^{\circ }<\frac{9C}{5}<{45}^{\circ }$

$\Rightarrow {180}^{\circ }<9C<{225}^{\circ }\Rightarrow {20}^{\circ }<C<{25}^{\circ }$

Thus the range of temperature between ${20}^{\circ }C$ and ${25}^{\circ }C$.