Question

will rent a car for a day. the rental company offers two pricing options: option a and option b. for each pricing option, cost (in dollars) depends on miles driven, as shown below.
(a) if ivan drives the rental car 150 miles, which option costs less?
option a option b
how much less does it cost than the other option?
$square$
(b) for what number of miles driven do the two options cost the same?
$square$
if ivan drives less than that amount, which option costs less?
option a option b

Explanation:

Part (a)

Step1: Analyze Option A at 150 miles

From the graph, Option A is a line with a slope. Let's assume the y - axis is cost (in dollars) and x - axis is miles driven. At \(x = 150\) miles, looking at the graph, the cost for Option A is around \(80\) dollars (from the red line).

Step2: Analyze Option B at 150 miles

Option B is a horizontal line. From the graph, the cost for Option B is \(50\) dollars (from the blue line).

Step3: Compare costs and find difference

Since \(50<80\), Option B costs less. The difference in cost is \(80 - 50=30\) dollars.

Step1: Find intersection of two lines

The two pricing options (Option A and Option B) are represented by two lines on the graph. The point where the two lines intersect is the point where they cost the same. From the graph, we can see that the two lines intersect at \(x = 50\) miles (by looking at the x - coordinate of the intersection point).

Answer:

Option B costs less. It costs \(\$30\) less than Option A.

Part (b)