Question

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​

Answer 1

Answer:

a. Angel has a greater flat fee

b. Difference = $130

Step-by-step explanation:

Given

Rose:

$Flat\ Fee = \ 50$

$Rate = \ 12$

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:

$Flat\ Fee = \ 50$

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

Start by calculating the slope (m) of the table

$m = \frac{y_2 - y_1}{x_2 - x_1}$

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

$(x_1,y_1) = (10, 180)$

$(x_2,y_2) = (30, 480)$

So: $m = \frac{y_2 - y_1}{x_2 - x_1}$ becomes

$m = \frac{480 - 180}{30 - 10}$

$m = \frac{300}{20}$

$m = 15$

Next, we calculate the equation using:

$y - y_1 = m(x - x_1)$

Where

$m = 15$

$(x_1,y_1) = (10, 180)$

$y - 180 = 15(x - 10)$

$y - 180 = 15x - 150$

Add 180 to both sides

$y - 180 + 180 = 15x - 150 + 180$

$y= 15x + 30$

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

$Flat\ Fee = \ 30$

$Rate = \ 15$

and

Rose:

$Flat\ Fee = \ 50$

$Rate = \ 12$

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:

$y= 15x + 30$

and x = 50.

So:

$y = 15 * 50 + 30$

$y = 750 + 30$

$y = 780$

For Rose,

First, we need to determine the equation.

$Flat\ Fee = \ 50$

$Rate = \ 12$

The equation is:

$y = Flat\ Fee + Rate * x$

$y = 50 + 12 * x$

So, the total charges for 50 guests is:

$y = 50 + 12 * 50$

$y = 50 + 600$

$y = 650$

The difference is then calculates as:

$Difference = 780 - 650$

$Difference = \ 130$