Question: Ahmad can choose Plan A or Plan B for his long distance charges. For each plan, cost (in dollars)…

Ahmad can choose Plan A or Plan B for his long distance charges. For each plan, cost (in dollars) depends on minutes used (per month) as shown below.

[Graph of Plan A and Plan B]

Cost (in dollars)

[Graph showing two lines: Plan A and Plan B, with cost on the y-axis and minutes used (per month) on the x-axis]

(a) If Ahmad makes 50 minutes of long distance calls for the month, which plan costs less?

• Plan A
• Plan B

How much less does it cost than the other plan? $ [Blank]

(b) For what number of long distance minutes do the two plans cost the same? [Blank]

If the time spent on long distance calls is less than this amount, which plan costs more? [Blank]

Solution

The problem involves interpreting the graphs of two functions, Plan A and Plan B, for cost based on minutes used. (a) If Ahmad makes 50 minutes of long-distance calls for the month, which plan costs less, and how much less does it cost than the other plan? To solve this, we need to read the cost from the graph for 50 minutes for both plans and compare them. From the graph: - For 50 minutes, Plan A costs $30. - For 50 minutes, Plan B costs $20. Plan B costs less. The difference in cost: \[ 30 - 20 = 10 \] Plan B costs $10 less than Plan A. (b) For what number of long-distance minutes do the two plans cost the same? To find when the costs are equal, determine where the lines intersect on the graph. From the graph, the lines intersect at around 100 minutes. Thus, the two plans cost the same at 100 minutes.