The formula c = 5p + 210 relates c, the total cost in dollars of hosting a birthday party at a skating rink, to p, the number of people attending. If Allie's parents are willing to spend $350 for a party, how many people can attend?

28 people

Step-by-step explanation:

Plug in 350 as c into the equation, since c is the total cost:

c = 5p + 210

350 = 5p + 210

Solve for p:

140 = 5p

28 = p

So, 28 people can attend

The correct option is c. The given system is inconsistent.

Step-by-step explanation:

Inconsistent system: If the given system has no solutions, then it is an inconsistent system.

Consistent and independent system: If the given system has only one solutions, then it is an consistent and independent system.

Consistent and dependent system: If the given system has many solutions, then it is an consistent and dependent system.

The given equations are

      ... (1)

Divide the second equation by 2, to rewrite the given equation in slope intercept form.

      ..... (2)

The slope intercept form of a line is

      ....(3)

Where, m is slope and b is y-intercept.

On comparing the (1), (2) and (3), we get the slope of first line is 0.5 and slope of second line is 0.5.

Since the slope of two parallel lines are same, therefore both the given equations are parallel and parallel equations have no solutions.

Therefore option c is correct.