Question

The current temperature is 73°F. It is expected to drop 3.5°F each hour. Define a variable and write an equation that can be used to find the number of hours it will take for the temperature to reach 59°F. Then solve the equation

Answer 1

Step 1

Given;

$\begin{gathered} \text{Current temperature=73}\degree F \\ \text{Expected drop per hour=3.5}\degree F \end{gathered}$

Required; To define a variable and write an equation that can be used to find the number of hours it will take for the temperature to reach 59°F.

Step 2

Let the variable use to represent the hour be x

We model the required equation using the model of the equation of a line.

$\begin{gathered} c(x)=73-3.5x_{} \\ x=\text{ number of hours} \\ c(x)=\text{Temperature at a given hour} \end{gathered}$

Step 3

Find the number of hours it will take for the temperature to reach 59°F.

$\begin{gathered} c(x)=59 \\ x=\text{?} \\ c(x)=73-3.5x \\ 59=73-3.5x \end{gathered}$$\begin{gathered} -14=-3.5x \\ \frac{-3.5x}{-3.5}=\frac{-14}{-3.5} \\ x=4\text{hours} \end{gathered}$

Hence, it will take 4 hours for the temperature to drop to 59°F.