Question

Triangle truck rentals charges 35 per day and 35 cents a mile. Circle rent a truck charges $60 a day and 30 cents a mile. How far would he need to drive in one day for both the companies to have the same total cost?

Answer 1

From the information given in the statement we know that:

• Triangle truck rentals charge ,$35 per day and 35 cents a, mile,.

,

• Circle rent a truck charge ,$60 a day and 30 cents a ,mile,.

On the other hand, let be x the number of miles he would need to drive in one day. So, we can write the following equation:

$\begin{gathered} \text{ Triangle truck rental charge }=\text{ Circle truck rental charge} \\ \text{\ }35+\text{\ }0.35x=\text{\ }60+\text{\ }0.30x \end{gathered}$

Now, we can solve the equation for x

$\begin{gathered} \text{\ }35+\text{\ }0.35x=\text{\ }60+\text{\ }0.30x \\ \text{ Subtract \ }0.30x\text{ from both sides of the equation} \\ \text{\ }35+\text{\ }0.35x-\text{\ }0.30x=\text{\ }60+\text{\ }0.30x-\text{\ }0.30x \\ \text{\ }35+\text{\ }0.05x=\text{\ }60 \\ \text{ Subtract \ 35 from both sides of the equation } \\ \text{\ }35+\text{\ }0.05x-\text{\ }35=\text{\ }60-\text{\ }35 \\ \text{\ }0.05x=\text{\ }25 \\ \text{ Divide by \ 0.05 from both sides of the equation} \\ \frac{\text{\ }0.05x}{\text{\ }0.05}=\frac{\text{\ }25}{\text{\ }0.05} \\ \mathbf{x=500} \end{gathered}$

Therefore, he would need to drive 500 thousand in one day for both companies to have the same total cost