Question

A solution is to be kept between 86° and 95°F. What is the range of temperature in degree Celsius, if the Celsius (C)/ Fahrenheit (F) conversion formula is given by $F=\frac{9}{5}C+32$.

Answer 1

Suppose the temperature of the solution is x degree Celsius.
∴ x in Fahrenheit = $\frac{9}{5}x+32$
Then, as per the given condition:

$$\begin{gathered} 86<\frac{9}{5}x+32<95 \\ \Rightarrow 86-32<\frac{9}{5}x<95-32(\mathrm{Subtratcting}32\mathrm{throughout}) \\ \Rightarrow 54<\frac{9}{5}x<63 \\ \Rightarrow \frac{5}{9}\times 54<\frac{5}{9}\times \frac{9}{5}x<\frac{5}{9}\times 63(\mathrm{Multiplying}\mathrm{by}\frac{5}{9}\mathrm{throughout}) \\ \Rightarrow 30<x<35 \\ \mathrm{Hence},\mathrm{the}\mathrm{range}\mathrm{of}\mathrm{the}\mathrm{temperature}\mathrm{in}\mathrm{degree}\mathrm{Celsius}\mathrm{is}\mathrm{between}30°\mathrm{C}\mathrm{and}35°\mathrm{C}. \end{gathered}$$