A restaurant offers a catering service which costs $25.00 per person with a $119.50 service charge. For parties of 50 or more people, a group discount applies, and the cost is $20.00 per person along with the service charge dropping to $59.00. (a) Write a piecewise-defined linear function which calculates the total cost T of the catering service which serves n people.

T1(n) = 25n +119.50  where n belongs to .

T2(n) = 20n + 59 where n belongs to .

Step-by-step explanation:

We are given two situations first is for normal days and the other is for days when 50 or more people are going to this restaurant for the party.

Let the number of person going for this restaurant be "n"

For normal day, we are given

catering service = $25 per person

service charge = $119.50  

Let the total cost of the restaurant be T

Cost for this case will be T1  

T1(n) = 25n +119.50  where n belongs to

similarly for the case when 50 or more than that goes to this restaurant for party.

cost after discount

Catering service = $20.00 per person

service charge = $59.00

now the cost of this case will be T2

T2(n) = 20n + 59 where n belongs to .

Therefore the two piecewise linear functions represents the total cost of the restaurant for serving n people.  

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step-by-step explanation: