Question

A rental car agency charges a flat fee of $160 plus $24 per day to rent a certain car. Another agency charges a fee of $48 plus $ 40 per day to rent the same car. Find the number of days for which the cost are the same.

Answer 1

7 days

Step-by-step explanation:

The first agency charges a flat fee of $160 plus $24 per day, so the equation that gives us the total cost for the first agency after x days is:

`C_1=160+24x`

At the same way, the equation that gives us the total cost for the second agency after x days is:

`C_2=48+40x`

Now, we need to find x, when C1 and C2 are equal, so we can write the following equation:

`\begin{gathered} C_1=C_2 \\ 160+24x=48+40x \end{gathered}`

So, solving for x, we get:

`\begin{gathered} 160+24x\textcolor{#FF7968}{-24x}=48+40x\textcolor{#FF7968}{-24x} \\ 160=48+16x \\ 160\textcolor{#FF7968}{-48}=48+16x\textcolor{#FF7968}{-48} \\ 112=16x \\ \frac{112}{\textcolor{#FF7968}{16}}=\frac{16x}{\textcolor{#FF7968}{16}} \\ 7=x \end{gathered}`

Therefore, if you rent a car for 7 days, the cost of both agencies will be the same.