Chapter A, Problem 27E

The relationship between the Celsius and Fahrenheit temperature scales is given by $C=\frac{5}{9}(F-32)$, where C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit. What interval on the Celsius scale corresponds to the temperature range 50 ≤ F ≤ 95?

To determine

To find: The interval on the Celsius scale corresponding to temperature range.

Answer to Problem 27E

The interval on the Celsius scale is $\left[10,35\right]$.

Explanation of Solution

Given:

The relationship between Celsius and Fahrenheit is $C=\frac{5}{9}\left(F-32\right)$.

Calculation:

Rewrite the given equation as,

$\begin{array}{l}C=\frac{5}{9}\left(F-32\right)\\ 9C=5F-160\\ 9C+160=5F\\ F=\frac{9C+160}{5}\end{array}$

It is given that, the Fahrenheit lies between 50 and 95. That is, $50\le \frac{9C+160}{5}\le 95$.

$\begin{array}{l}50\le \frac{9C+160}{5}\le 95\\ 250\le 9C+160\le 475\\ 90\le 9C\le 315\\ 10\le C\le 35\end{array}$

Thus, the interval on the Celsius scale is $\left[10,35\right]$.