Question

you need to rent a moving truck for a day. you have identified two companies that rent trucks. company a charges $40 per day plus $0.20 per mile. company b charges $35 per day plus $0.25 per mile. for how many miles will the cost of renting be the same?

Explanation:

Step1: Set up cost - equations

Let $x$ be the number of miles. The cost $C_A$ of Company A is $C_A = 40+0.20x$. The cost $C_B$ of Company B is $C_B=35 + 0.25x$.

Step2: Set the two cost - equations equal

We want to find when $C_A = C_B$, so $40+0.20x=35 + 0.25x$.

Step3: Solve for $x$

Subtract $0.20x$ from both sides: $40=35 + 0.25x-0.20x$.
Simplify the right - hand side: $40=35 + 0.05x$.
Subtract 35 from both sides: $40 - 35=0.05x$.
We get $5 = 0.05x$.
Divide both sides by 0.05: $x=\frac{5}{0.05}=100$.

Answer:

100