Question

At what temperature will the reading on the Fahrenheit scale be five times that on the Celsius scale?

Answer 1

The relation between the Fahrenheit and centigrade is linear in nature. We will use the relation between the two scales and place the value of temperature given in the question

Formula used: In this solution, we will use the following formula:
$C = \dfrac{5}{9}(F - 32)$ where $C$ is the temperature in the centigrade scale and $F$ is the temperature in Fahrenheit scale.

Complete step by step answer
The relation between the temperature of an object in centigrade and Fahrenheit is given as:
$C = \dfrac{5}{9}(F - 32)$
We want to find the point where the reading on the Fahrenheit scale is five times that on the Celsius scale. This implies that we can write $F = 5C$ . Substituting this value in the above equation, we get
$C = \dfrac{5}{9}(5C - 32)$
Multiplying both sides by $9$ , we get
$9C = 5(5C - 32)$
Solving for $C$ , we get
$25C - 9C = 160$
Simplifying the above term, we get
$16C = 160$
Which give us
$C = 10^\circ$ .

Additional information
In the Fahrenheit scale, the reference temperatures are $32\;^\circ F$ as a freezing point of water and $212\;^\circ F$ as a boiling point of water. Whereas in the Celsius scale $0\;^\circ C$ is the freezing point of water and $100\;^\circ C$ is the boiling point of water. Both scales are related directly and linearly which means that if the temperature of an object rises, its value rises both in the centigrade and in the Fahrenheit scale. The common point of both scales is $- 40^\circ C$ which means that both the centigrade and the Fahrenheit scales will have the same value i.e. $- 40^\circ C = - 40^\circ F$ .

Note
We must know the conversion of different temperature scales to answer such questions. Celsius and Fahrenheit are the most widely used temperature scales worldwide along with the Kelvin scale so we must at least know their interconversions.