Question

Mrs. Nix is having a birthday party for her daughter Rebecca. Rebecca wants to have a gymnastics party so Mrs. Nix looks into ENA and Paragon. Paragon requires a $20 fee for party favors and set-up and charges $24.95 per child to attend the party. ENA charges a $60 fee for party favors and set-up and then charges $19.95 per child to attend the party. Which gym should Mrs. Nix choose for Rebecca to have her party? She isn't sure how many guests are coming yet!

Answer 1

To determine which gym Mrs. Nix should choose for Rebecca's party, we need to compare the total cost for both options. ENA is the cheaper option.

Step-by-step explanation:

To determine which gym Mrs. Nix should choose for Rebecca's party, we need to compare the total cost for both options. Let's start by calculating the total cost for Paragon:

1. Party favors and set-up fee: $20
2. Total cost per child: $24.95

Since we don't know how many guests will be attending, we can represent the total cost for Paragon as follows: C = 20 + 24.95x, where x is the number of children.

Now, let's calculate the total cost for ENA:

1. Party favors and set-up fee: $60
2. Total cost per child: $19.95

Similarly, the total cost for ENA can be represented as C = 60 + 19.95x.

To determine which gym is cheaper, we need to compare the slopes of the two equations. The slope of the Paragon equation is $24.95 and the slope of the ENA equation is $19.95. Since $19.95 is less than $24.95, ENA is the cheaper option. Therefore, Mrs. Nix should choose ENA for Rebecca's party.