Question

Company A charges a flat rate of $100 plus $0.30 per mile to rent a truck. Company B charges a flat rate of $200 plus $0.10 per mile to rent the same truck. After how many miles do both companies to charge the same amount?

Answer 1

After setting up equations for both companies' charging rates and solving for x, which represents the number of miles, we find that after 500 miles, both companies will charge the same amount to rent a truck.

Step-by-step explanation:

To find out how many miles both Company A and Company B charge the same amount to rent a truck, we need to set up an equation where the total cost from Company A equals the total cost from Company B.

Let's denote the number of miles driven as x. For Company A, the cost is $100 plus $0.30 per mile, so their formula for cost is 100 + 0.30x. For Company B, the cost is $200 plus $0.10 per mile, so their cost formula is 200 + 0.10x. We want to find the point where these two costs are equal, thus:

100 + 0.30x = 200 + 0.10x

Solving for x, we subtract 0.10x from both sides to get 0.20x and subtract 100 from both sides to get 100:

0.20x = 100

And then we divide both sides by 0.20:

x = 500 miles.

This means after 500 miles, both Company A and Company B will charge the same amount to rent the truck.