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