Question

Student Council sponsors weekly dances at their school on Friday nights. The admission price for each person is $4 for Student Council members. Members pay an annual fee of $50 for membership dues.
A. Write a function that can be used to determine c, the total cost, for a member to attend n, number of dances a year.

B. How much will a member pay if they attend 15 dances during the school year.

1. Summarize the given situation in your own words. (What do you notice?)

2. Explain: What is the essential information you can use to find the solution?

3. Find the Solutions to parts A and B above. Show your thinking in the space below.

Answer 1

The total cost during a school year to attend a given number of daces is a

linear function of the number of dances attended.

The correct responses are;

• Part A; The function for the total cost is; c = 50 + 4·n

• Part B; The total cost for attending 15 dances is; c = $110

• 1. The initial cost is $50 and the rate is $4

• 2. The annual fee, the admission price, and the number of dances attended

• 3. The solution are: Part A; c = 50 + 4·n, Part B; c = $110

Reasons:

The given parameter are;

Admission price per person = $4

The annual fees members pay = $50

A. The function that can be used to determine c is a linear function, with a y-intercept (initial value) of 50 and a rate (slope) of 4

The total cost to attend n dances a year, c = 50 + 4·n

B. If a member attends 15 dances a year, we have;

n = 15

Therefore;

The total cost, c = 50 + 4 × 15 = 110

The total cost for 15 dances a year, c = $110

1. As the number of dances attended increase, the total cost increase, and the cost when no dance is attended by a member during the year is $50.

2. The essential information that can be used to find the solution are;

• The admission price for each person.

• The annual fee for membership dues.

• The number of dances a member attends in a year.

3. Part A; c = 50 + 4·n

Part B; c = $110

Learn more about linear functions here:

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