Question

The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation $C=\dfrac{5F-160}{9}$.
If the temperature is 86F, what is the temperature in Celsius?
\[\begin{align}
  & A.40 \\
 & B.30 \\
 & C.20 \\
 & D.70 \\
\end{align}\]

Answer 1

Hint: In this question, we are given a conversion relation between Celsius (C) and Fahrenheit (F). We need to find temperature in Celsius if the temperature in Fahrenheit is 86F. For this, we just need to put the value of F as 86 in the given formula and calculate the temperature in Celsius.

Complete step-by-step answer:
Here, the linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation $C=\dfrac{5F-160}{9}$.
We need to find the temperature in Celsius if the temperature in Fahrenheit is 86F.
So putting the value of F as 86 in the given formula will give us the value of C which will be the temperature in Celsius.
Let us put F as 86 in the formula we get $C=\dfrac{5\left( 86 \right)-160}{9}$.
As we know, that $86\times 5$ is equal to 430 so our equation becomes $C=\dfrac{430-160}{9}$.
Now subtracting 160 from 430, we get 430-160 = 270. Hence our equation reduces to $C=\dfrac{270}{9}$.
Now 270 is divisible by 3 (2+7 = 9 is divisible by 3) and 9 is also divisible by 3, so dividing the numerator and the denominator by 3, we get $C=\dfrac{90}{3}$.
Now we know 3 divides 90 so we get $C=30$.
So we get the value of C as 30 which is the temperature in Celsius.
Hence 86F is equal to 30C.

So, the correct answer is “Option B”.

Note: Students should solve the equation carefully. Always solve numerator first and then divide it by the denominator. Students can make mistake in signs while solving. We have used divisibility rule of 3 to state that 270 is divisible by 3. Divisibility rule of 3 states that if the sum of the sum of the digits of a number is divisible by 3 then the number is divisible by 3.