Question

In countries like the USA and Canada the temperature is measured in Fahrenheit whereas in countries like India it is measured in Celsius. Here is a linear equation that converts Fahrenheit into Celsius, \[F = \left( {\dfrac{9}{5}} \right)C + 32\]. If the temperature is \[{0^ \circ }C\] then what is the temperature in Fahrenheit and if the temperature is \[{0^ \circ }F\] what is the temperature in Celsius.
A. \[ - {32^ \circ }F,{17.7^ \circ }C\]
B. \[{32^ \circ }F,{17.7^ \circ }C\]
C. \[ - {32^ \circ }F, - {17.7^ \circ }C\]
D. \[{32^ \circ }F, - {17.7^ \circ }C\]

Answer 1

Hint:Here we use the conversion equation given in the question to find the values in both situations. First we substitute temperature in Celsius as zero and find temperature in Fahrenheit. And then we substitute temperature in Fahrenheit as zero and find temperature in Celsius.
* Both Celsius and Fahrenheit are measured in degree.
* From Fahrenheit to Celsius we subtract \[32\]and multiply the remainder by \[\dfrac{5}{9}\]
* From Celsius to Fahrenheit we multiply by \[\dfrac{9}{5}\] and then add \[32\]

Complete step-by-step answer:
We are given the linear equation of conversion of temperature as \[F = \left( {\dfrac{9}{5}} \right)C + 32\]
Here temperature in Fahrenheit is denoted by \[F\] and temperature in Celsius is denoted by \[C\].
When temperature is \[{0^ \circ }C\] then we substitute the value of \[C = 0\]in the equation
\[
  F = \left( {\dfrac{9}{5}} \right) \times 0 + 32 \\
  F = 0 + 32 \\
  F = 32 \\
 \] { Whenever any number is multiplied to zero the number becomes zero}
So, when the temperature is \[{0^ \circ }C\] then temperature is \[{32^ \circ }F\]
Now when we are given the temperature as \[{0^ \circ }F\] then we substitute the value of \[F = 0\] in the equation.
\[0 = \left( {\dfrac{9}{5}} \right)C + 32\]
Shifting the constant value to LHS
\[ - 32 = \left( {\dfrac{9}{5}} \right)C\]
Now, we multiply both sides of the equation by \[\dfrac{5}{9}\] which will help us to find the value of \[C\].
\[ - 32 \times \dfrac{5}{9} = \dfrac{9}{5} \times \dfrac{5}{9}C\]
Cancel out the same terms from numerator and denominator on RHS of the equation.
 \[
  \dfrac{{ - 160}}{9} = C \\
  C = - 17.7 \\
 \]
So, when the temperature is \[{0^ \circ }F\] then temperature is \[ - {17.7^ \circ }C\].
So, option D is correct.

Note:Students are likely to make the mistake of not writing the unit along with the value in the final answer. Also, calculations should be done carefully keeping in mind that sign changes from negative to positive and vice versa when shifted from one side of the equation to another side.