At Maple High, the cost to attend special events depends on whether a student has purchased a $10 discount card. Option A: The student buys a discount card. The cost is $5 per event. Option B: The student does not buy a discount card. The cost is $7.50 per event.

a. See the attached picture for the graph and the excel file for how the graph is drawn.

b. The students at Maple High should choose Option A when attending more than 4 events; but they should choose Option B when attending less than 4 events

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

At Maple High, the cost to attend special events depends on whether a student has purchased a $10 discount card.

Option A: The student buys a discount card. The cost is $5 per event.

Option B: The student does not buy a discount card. The cost is $7.50 per event.

a. Graph the relationship between total cost and number of events for each option.

b. Determine the condition under which the students at Maple High should chose each option.

The explanations to the answers is now given as follows:

Let x represent the number of events and y represents the total cost.

Options A and B can therefore be written as follows:

Option A: y = 5x + 10 ……………………………. (1)

Option B: y = 7.5x ……………………………….. (2)

a. Graph the relationship between total cost and number of events for each option.

Note: See the attached picture for the graph and the excel for how the graph is drawn.

In the excel, we assume figures for x from 1 to 10 and then calculate the associated y using equations (1) and (2) above

Also, the number of events (x) is on the horizontal axis while the total cost (y) is on the vertical axis.

The graph for Option A is the blue one while the graph for Option B is the red one.

b. Determine the condition under which the students at Maple High should chose each option.

From the graph in the picture and the attached excel file, the total costs (y) for each of Options A and B ar equal when the number of events (x) is equal to 4.

It can bee observed that when the number of events (x) is greater than 4, the total cost (y)  of Option A is less than the total cost (y) of Option B. Under this condition, Option A should be chosen.

On the other hand, when the number of events (x) is less than 4, the total cost (y)  of Option A is greater than the total cost (y) of Option B. Under this condition, Option B should be chosen.

Therefore, the students at Maple High should choose Option A when attending more than 4 events; but they choose Option B when attending less than 4 events.