Question

Nolan is deciding between two truck rental companies. Company A charges an initial fee of $15 for the rental plus $1.50 per mile driven. Company B charges an initial fee of $35 for the rental plus $1 per mile driven. Let A represent the amount Company A would charge if Nolan drives x miles, and let B represent the amount Company B would charge if Nolan drives x miles. Graph each function and determine the interval of miles driven, x, for which Company A is cheaper than Company B.

Answer 1

To find the interval of miles driven for which Company A is cheaper than Company B, we set the cost functions for both companies and solve for x. The interval is x < 40.

Step-by-step explanation:

To determine the interval of miles driven, x, for which Company A is cheaper than Company B, we need to compare the cost functions of both companies. Let's represent the cost for Company A as A(x) and the cost for Company B as B(x).

For Company A, the cost function is A(x) = 15 + 1.5x, where x represents the number of miles driven. For Company B, the cost function is B(x) = 35 + x.

To find the interval of x for which Company A is cheaper than Company B, we need to set A(x) < B(x) and solve for x.

Setting A(x) < B(x), we have 15 + 1.5x < 35 + x. Simplifying the inequality gives us 0.5x < 20, or x < 40.

Therefore, Company A is cheaper than Company B for any number of miles driven less than 40.