Question

A bottle of medicine is to be stored at a temperature between $5^{°}\mathrm{C}\mathrm{and}{10}^{°}\mathrm{C}$. What range does this correspond to on the Fahrenheit scale?

Short answer

The medicine should be stored at a temperature between${41}^{°}\mathrm{F}\mathrm{and}{50}^{°}\mathrm{F}$

Step-by-step solution

Step 1. Relationship between Fahrenheit and Celsius.

The relationship between degrees Celsius$\left(\mathrm{C}\right)$and degrees Fahrenheit$\left(\mathrm{F}\right)$is given by the equation

$\mathrm{C}=\frac{5}{9}(\mathrm{F}-32)$

Step 2. Expressing the statement in terms of inequality.

Now, expressing the statement on the bottle in terms of inequalities, we have $5<\mathrm{C}<10$

Step 3. Determining the range.

$\begin{array}{l}5<\frac{5}{9}(\mathrm{F}-32)<10(\mathrm{Substitute}\mathrm{C}=\frac{5}{9}(\mathrm{F}-32\left)\right)\\ \frac{9}{5}.5<\frac{9}{5}.\frac{5}{9}(\mathrm{F}-32)<10.\frac{9}{5}(\mathrm{Multiply}\mathrm{by}\frac{9}{5})\\ 9<\mathrm{F}-32<18\left(\mathrm{Simplify}\right)\\ 9+32<\mathrm{F}-32+32<18+32\left(\mathrm{Add}32\right)\\ 41<\mathrm{F}<50\left(\mathrm{Simplify}\right)\end{array}$