Question

The expression for degrees Fahrenheit is $\left(\frac{9}{5}C+32\right)$ where $C$ represents degrees Celsius. The temperature today is $5$ degrees Celsius more than yesterday. Write and simplify an expression for the difference in degrees Fahrenheit for these two days.

Answer 1

Formation and simplification of algebraic expression :

The expression for degrees Fahrenheit is $=\frac{9}{5}C+32$

Now, according to question:

The temperature today is $5$ degrees Celsius more than yesterday.

Let yesterday’s tempearture in degrees was $=x$

Then yesterday's temperature in Fahrenheit is $=\frac{9}{5}x+32$

And today’s temperature in Fahrenheit is $=\frac{9}{5}(x+5)+32$

The difference in degrees Fahrenheit for these two days :

$$\begin{gathered} =\frac{9}{5}(\mathrm{x}+5)+32-\left(\frac{9}{5}\mathrm{x}+32\right) \\ =\frac{9}{5}\left(\mathrm{x}\right)+\frac{9}{5}\left(5\right)+32-\frac{9}{5}\mathrm{x}-32\{\mathrm{Distributive}\mathrm{property}\} \\ =\frac{9}{5}\mathrm{x}+9+32-\frac{9}{5}\mathrm{x}-32\left\{\mathrm{Simplify}\right\} \\ =9 \end{gathered}$$

Hence, the difference in degrees Fahrenheit fro the two days is $9$ degree Fahrenheit.