Question

Good Eatz charges a fixed cost for preparing a dinner plus an additional cost for each student served. They quoted the cost of catering 100 students at $750, and 150 students at $1050.

A Cut Above has a fixed fee of $200, and they quoted $1300 for serving 200 students.

Write two different linear functions modeling the cost of each caterer, based on the number of students served. Make sure to define what x and y both represent.

Find the number of students served for which the cost of the two caterers is the same. Show your work

Answer 1

To find the linear function for Good Eatz, we can use the two data points: (100, $750) and (150, $1050). Solving the equations, we find that the linear function for Good Eatz is y = 3x + 450. To find the linear function for A Cut Above, we can use the data point (200, $1300). Solving the equation, we find that the linear function for A Cut Above is y = 5x + 300. The cost of the two caterers is the same when 75 students are served.

Step-by-step explanation:

Let's define:

1. x - The number of students served
2. y - The cost of catering

To find the linear function for Good Eatz, we can use the two data points: (100, $750) and (150, $1050). We can set up two equations using these data points:

100 = mx + b ---- (1)

150 = mx + b ---- (2)

Solving these equations simultaneously, we find that m = $3 and b = $450. Therefore, the linear function for Good Eatz is y = 3x + 450.

To find the linear function for A Cut Above, we can use the data point (200, $1300). We can set up an equation using this data point:

1300 = mx + b

Solving this equation, we find that m = $5 and b = $300. Therefore, the linear function for A Cut Above is y = 5x + 300.

Now, let's find the number of students served for which the cost of the two caterers is the same. We can set up an equation by equating the two linear functions:

3x + 450 = 5x + 300

Simplifying the equation, we find that x = 75. Therefore, the cost of the two caterers is the same when 75 students are served.