Question

Luis is deciding between two truck rental companies. Company A charges an initial fee of $40 for the rental plus $0.50 per mile driven. Company B charges an initial fee of $10 for the rental plus $1 per mile driven. Let A A represent the amount Company A would charge if Luis drives x x miles, and let B B represent the amount Company B would charge if Luis drives x x miles. Graph each function and determine the interval of miles driven, x , x, for which Company A is cheaper than Company B.

Answer 1

The function for Company A is A(x) = 0.5x + 40, and the function for Company B is B(x) = x + 10.

To determine the interval of miles driven for which Company A is cheaper than Company B, we need to find the values of x for which A(x) < B(x).

0.5x + 40 < x + 10

0.5x < 30

x < 60

So Company A is cheaper than Company B for values of x less than 60.

To graph the functions, we can plot points for different values of x:

For Company A:
x = 0, A(x) = 40
x = 10, A(x) = 45
x = 20, A(x) = 50
x = 30, A(x) = 55
x = 40, A(x) = 60

For Company B:
x = 0, B(x) = 10
x = 10, B(x) = 20
x = 20, B(x) = 30
x = 30, B(x) = 40
x = 40, B(x) = 50

We can then plot these points and draw a line through them for each function. The point of intersection is (60, 70), which is the point at which the two functions are equal.

We can see that for values of x less than 60, the line for Company A is below the line for Company B, which means that A(x) < B(x) and Company A is cheaper. For values of x greater than 60, the line for Company B is below the line for Company A, which means that B(x) < A(x) and Company B is cheaper.