Question

Water boils at $212^\circ F$ or $100^\circ C$ and melts at $32^\circ F$ or $0^\circ C$. If the temperature on a particular day is $35^\circ C$, then the equivalent value on the Fahrenheit scale is:
A. $95F$
B. $85F$
C. $99F$
D. $90F$

Answer 1

Hint: In order to solve the problem, create a random relation between the temperature in Fahrenheit and the temperature in Celsius. Then find the value of the constants by using the conditions given in the question. At last find the temperature in Fahrenheit when it is $35$ in Celsius.

Complete step-by-step answer:
Let us assume the relation between temperature in Celsius and the temperature in Fahrenheit which is:
$F = aC + b$$ - - - - (1)$
Where $F$ is the temperature in Fahrenheit
$C$ is the temperature in Celsius.
Here a, b are the constants.
Now the question says that it melts at $32^\circ F$ or $0^\circ C$ which means that when $C = 0^\circ ,F = 32^\circ $
Using it in (1)
$a(0) + b = 32^\circ $
$b = 32^\circ $
Now the equation (1) becomes
$F = aC + 32^\circ $$ - - - - (2)$
Next we are also given in the question that water boils at $212^\circ F$ or $100^\circ C$
This means that when $C = 100^\circ ,F = 212^\circ $
Using it in equation (2)
$a(100^\circ ) + 32^\circ = 212^\circ $
$a(100^\circ ) = 180^\circ $
$a = \dfrac{9}{5}$
Hence the relation between $F,C$ is:
$F = \dfrac{9}{5}C + 32^\circ $
Now we need to find $F$ when $C$ is $35^\circ $
$F = \dfrac{9}{5}(35) + 32^\circ $
$F = 95^\circ $
Therefore when in Celsius the temperature is $35^\circ $, then the temperature in Fahrenheit is $95^\circ $

Note: Although we derived the relation between the temperature in Celsius and Fahrenheit in this question, this formula must also be remembered as it may not be given in some other problems. We also need to remember the relation between Celsius and kelvin.