Adrienne had a party at a local swimming pool. She spent fifty dollars for a pavilion and seven dollars per person for admission. Let c be the total cost of the pavilion and admission, and let p be the number of people at her party. Write an equation to represent the problem. Which is the independent variable? Explain.

C= 7p + 50

C represent the total cost of the party, and 7p represents the cost depending upon the number of people attending. The independent variable would be p, people, because Adrienne can change the number of people, it is independent of the other variable. Variable C is dependent upon the number of people, p. This is very, very easy.

To write an equation to represent the problem, we can start by breaking down the costs involved.

We know that Adrienne spent $50 for the pavilion and $7 per person for admission. Let's use c to represent the total cost of the pavilion and admission, and p to represent the number of people at her party.

The cost of the pavilion is a fixed amount, which is $50. So, we can write the cost of the pavilion as a constant, 50.

The cost of admission per person is $7. Since the number of people at the party may vary, we can express the cost of admission as 7 times the number of people, which gives us 7p.

To calculate the total cost (c) of the pavilion and admission, we need to add the cost of the pavilion ($50) to the cost of admission (7p):

c = 50 + 7p

In this equation, the independent variable is p, which represents the number of people at the party. The independent variable is the one that can be changed or varied in the equation. In this case, Adrienne can control the number of people she invites to the party, and the cost will depend on this number. The cost (c) is dependent on the number of people (p), so p is the independent variable.