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

a. Angel has a greater flat fee

b. Difference = $130

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 = (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 = (y_2 - y_1)/(x_2 - x_1)` becomes

`m = (480 - 180)/(30 - 10)`

`m = (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`