Question

A solution is to be kept between ${40}^{\circ }$ C and ${45}^{\circ }$ C . What is the range of temperature in degree Fahrenheit, if the conversion formula is

$F=\frac{9}{5}C+32?$

Answer 1

Given : $F=\frac{9}{5}C+32?$

$\Rightarrow 5F=9C+160$

$\Rightarrow C=\frac{5F-160}{9}$

$\because$ Temperature in degree Celsius lies between ${40}^{\circ }$ C to ${45}^{\circ }$ C

$\Rightarrow {40}^{\circ }<\frac{5F-160}{9}<{45}^{\circ }$

$\Rightarrow {360}^{\circ }<5F-160<{405}^{\circ }$

$\Rightarrow {520}^{\circ }<5F<{565}^{\circ }$

$\Rightarrow {104}^{\circ }<F<{113}^{\circ }$

Hence, the range of temperature in degree Fahrenheit is ${104}^{\circ }Fto{113}^{\circ }F$.