Question
Calculate the temperature which has same numeral value on celsius and Fahrenheit scale.
✓
Answer
Let the required temperature is $x^0C = x^0F \frac{\text{C}}{100}=\frac{\text{F}-32}{180}$
$\Rightarrow\frac{\text{x}}{5}=\frac{\text{x}-32}{9}$
$\Rightarrow5\text{x}-160=9\text{x}$
$\Rightarrow-9\text{x}+5\text{x}=160$
$\Rightarrow-4\text{x}=160$
$\Rightarrow\text{x}=\frac{160}{-4}=-40^\circ$
$\therefore-40^\circ\text{F}=-40^\circ\text{C}$
$\Rightarrow\frac{\text{x}}{5}=\frac{\text{x}-32}{9}$
$\Rightarrow5\text{x}-160=9\text{x}$
$\Rightarrow-9\text{x}+5\text{x}=160$
$\Rightarrow-4\text{x}=160$
$\Rightarrow\text{x}=\frac{160}{-4}=-40^\circ$
$\therefore-40^\circ\text{F}=-40^\circ\text{C}$
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