Rose and Angel are caterers. Both Rose and Angel charge a flat fee plus a fee per guest. Rose charges a flat fee of $50 plus $12 per guest. The table shows how much Angel charges for different numbers of guests. Angel's Catering Charges Number of Guests Charge ($) 10 $180 15 $255 25 $405 30 $480 Part A Who charges the greater flat fee? O A. Rapse O B. Angel Part B Vhat is the difference in total charges between Angel and Rose for a party that includes 50 guests? Enter the answer in the box. Autohide sh Growth: Math 6+ GA 2015 Question ITU Shelf nositi

a. Angel has a greater flat fee

b. Difference = $130

Step-by-step explanation:

Given

Rose:

Angel

Guests --- Charges

10 -------- $180

15 -------- $255

25 -------- $405

30 -------- $480

Solving (a): Who charges the greater flat fee?

We have that the flat fee of Rose is:

For Angel, we need to determine the equation of the given table

Start by calculating the slope (m) of the table

Where x and y represent any two corresponding values of the guests and the charges.

So: becomes

Next, we calculate the equation using:

Where

Add 180 to both sides

From the equation above:

The slope = 15 --- This represents the hourly rate

and

y intercept = 30 --- This represents the flat fee

This is better represented as:

Angel

and

Rose:

By comparison, Angel has a greater flat fee

Solving (b): Difference between total charges of 50 guests for both caterers.

For angel, the equation is:

and x = 50.

So:

For Rose,

First, we need to determine the equation.

The equation is:

So, the total charges for 50 guests is:

The difference is then calculates as:

what