Question

a man is considering two companies from which to rent a truck. triangle truck rental charges $25 per day and 25 cents a mile. circle rent - a - truck charges $40 a day and 15 cents a mile. how far would he need to drive in one day for the both companies to have the same total cost? how many miles would he need to drive in the day? miles

Explanation:

Step1: Set up cost - equations

Let $x$ be the number of miles driven. The cost $C_1$ for Triangle Truck Rental is $C_1 = 25+0.25x$ (25 dollars per day plus 0.25 dollars per mile). The cost $C_2$ for Circle Rent - A - Truck is $C_2=40 + 0.15x$ (40 dollars per day plus 0.15 dollars per mile).

Step2: Set the two costs equal

We want to find when $C_1 = C_2$, so we set up the equation $25+0.25x=40 + 0.15x$.

Step3: Solve for $x$

Subtract $0.15x$ from both sides: $25+0.25x-0.15x=40 + 0.15x-0.15x$, which simplifies to $25 + 0.1x=40$. Then subtract 25 from both sides: $0.1x=40 - 25$, so $0.1x=15$. Divide both sides by 0.1: $x=\frac{15}{0.1}=150$.

Answer:

150