Robert wants to have his birthday party at a bowling alley with a few friends, but he can spend no more than $80. the bowling alley charges a flat fee of $45 for a private party and $5.50 per person for shoe rentals and unlimited bowling.

a. write an inequality that represents the total cost of roberts' birthday party given his budget.

b. how many people can robert pay for (including himself) while staying within the limitations of his budget?

The trick to solving this problem is to realize that the independent variable is x, which represents the number of people who can attend the party without the total party cost exceeding $80.

This is the form of the inequality:

(total cost) [less than or equal to] $80
(rent) + (cost per guest)(number of guests) [less than or equal to] $80
  $45  + $5.50 x                                            [less than or equal to] $80

Simplify.  To do this, subtract $45 from both sides of this inequality.

Divide both sides of the resulting inequality by $5.50.

What is the restriction on x?

The solution would be like this for this specific problem:

 

Dimensions of the rectangle = 12 + x and 14 + x

(12 + x) (14 + x) = 288

x² + 26x + 168 = 288

x² + 26x − 120 = 0

(x + 30) (x − 4) = 0

x=−30, x =4

 

The dimensions increased by 4 feet.

 

I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.