A solution is to be kept between 86° and 95°F. What is the range of temperature in degree Celsius,

Question:

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

Solution:

Suppose the temperature of the solution is $x$ degree Celsius.

$\therefore x$ in Fahrenheit $=\frac{9}{5} x+32$

Then, as per the given condition:

$86<\frac{9}{5} x+32<95$

$\Rightarrow 86-32<\frac{9}{5} x<95-32 \quad$ (Subtratcting 32 throughout)

$\Rightarrow 54<\frac{9}{5} x<63$

$\Rightarrow \frac{5}{9} \times 54<\frac{5}{9} \times \frac{9}{5} x<\frac{5}{9} \times 63 \quad$ (Multiplying by $\frac{5}{9}$ throughout)

$\Rightarrow 30

Hence, the range of the temperature in degree Celsius is between $30^{\circ} \mathrm{C}$ and $35^{\circ} \mathrm{C}$.

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