Question

kira 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 kira drives the rental car 150 miles, which option costs more?
option a option b
how much more does it cost than the other option?
$
(b) for what number of miles driven do the two options cost the same?

if kira drives less than this amount, which option costs more?
option a option b

Explanation:

Part (a)

Step1: Find cost of Option A at 150 miles

From the graph, Option A is a line. At 150 miles, looking at the y - axis (cost), Option A's cost is 65 dollars (since the line for Option A at x = 150 has y = 65).

Step2: Find cost of Option B at 150 miles

Option B is a horizontal line. Its cost is 50 dollars (since it's a horizontal line at y = 50).

Step3: Determine which is more and the difference

Since 65>50, Option A costs more. The difference is 65 - 50=15 dollars.

Step1: Find intersection of two lines

The two lines (Option A and Option B) intersect where their costs are equal. From the graph, the x - coordinate (miles driven) where they intersect is 100 miles (since the two lines cross at x = 100).

Step2: Determine which is more for less miles

For x < 100 (miles less than 100), we can see from the graph that Option B (the horizontal line at 50) is above Option A's line (which is increasing) for x < 100? Wait, no. Wait, Option A starts at (0,20) and increases, Option B is at (0,50) and stays. Wait, at x = 0, Option B is 50, Option A is 20. At x = 100, they are both 50. So for x < 100, Option B's cost (50) is more than Option A's cost (since Option A at x = 0 is 20, at x = 100 is 50, so for x < 100, Option A's cost is less than 50, and Option B's cost is 50). So if Kira drives less than 100 miles, Option B costs more.

Answer:

Option A; 15

Part (b)