Question

The linear equation is $F = \dfrac{9}{{5C}} + 32$ that converts Fahrenheit to Celsius. When Fahrenheit is equal to Celsius.

Answer 1

Hint We should know that a degree on the Fahrenheit scale is 1/180 of the interval between the freezing point and also the boiling point of water. With the help of this concept we can solve this question.

Complete step by step answer
We know that:
$F = \left( {\dfrac{9}{5}} \right)C + 32\;$
$F - 32 = \left( {\dfrac{9}{5}} \right)C\;$
$\left( {\dfrac{5}{9}} \right)\left[ {F - 32} \right] = C$
Now,
If F = C.
Then,
$C = \left( {\dfrac{5}{9}} \right)\left[ {C - 32} \right]$
$\Rightarrow 9C = 5\left( {C - 32} \right)$
$\Rightarrow 9C - 5C = - 160$
$\Rightarrow 4C = - 160$
$\Rightarrow C = \dfrac{{\left( { - 160} \right)}}{4}$
$\Rightarrow C = - {40^ \circ }$

Hence, the correct answer is $\;C = - {40^ \circ }$.

Note It should be known to us that on the Celsius scale, the freezing and the boiling point of water are 100 degrees apart. A time interval of 1 Fahrenheit is equal to an interval of 5/9 degrees Celsius.