the cost c of going to the movies varies directly with the number of people N attending. A group of four paid $14 to go to the movies on Friday. Write an equation that relates c & n. How much would it cost for seven people to go to the movies.

c = kN

From the data,

14 = 4k
k = 7/2

so,

c = 7/2 N

Now just plug in N=7 to get the cost.

cheap tickets! Must be an old problem, or a discount theater...

To write an equation that relates the cost (c) to the number of people attending (N), we can use the direct variation formula, which is of the form c = kN. Here, k represents the constant of variation.

We are given that a group of four people paid $14 to go to the movies. So, we can substitute these values into the equation to solve for k:

14 = k * 4

To solve for k, divide both sides of the equation by 4:

k = 14 / 4
k = 3.5

Now that we have the value of k, we can write the equation relating c and N:

c = 3.5N

To find out how much it would cost for seven people to go to the movies, substitute N = 7 into the equation:

c = 3.5 * 7
c = 24.5

Therefore, it would cost $24.50 for seven people to go to the movies.

The problem states that the cost, denoted as c, of going to the movies varies directly with the number of people, denoted as N, attending. When two quantities vary directly, it means that they can be related by multiplying one another by a constant. In this case, the constant is the cost per person.

Let's start by finding the constant of variation. We know that a group of four people paid $14 to go to the movies. So, we can set up the following equation:

c = kN,

where c is the cost, k is the constant of variation, and N is the number of people attending.

Substituting N = 4 and c = 14 into the equation, we get:

14 = k * 4.

To solve for k, we divide both sides of the equation by 4:

k = 14 / 4 = 3.5.

Now that we have the constant of variation, we can write the equation that relates c and N:

c = 3.5N.

To find how much it would cost for seven people to go to the movies, we substitute N = 7 into the equation:

c = 3.5 * 7 = $24.50.

Therefore, it would cost $24.50 for seven people to go to the movies.