A restaurant offers a catering service which costs $19.50 per person with a $91.75 service charge. For parties of 70 or more people, a group discount applies, and the cost is $15.00 per person along with the service charge dropping to $45.00. Write a piecewise-defined linear function which calculates the total cost T of the catering service which serves n people.

1. T=19.5n+91.75, where n<70

2. T=15n+45, where n≥70

Explanation:

1. The first linear function can be expressed as;

Total cost of catering services = (Cost per person*number of people, n) + Service charge

where;

Total cost of catering services=T

Cost per person=$19.50

Number of people=n

Service charge=$91.75

Replacing;

T = (19.5*n) + 91.75

T=19.5n+91.75

The first equation: T=19.5n+91.75, where n<70

2. The second linear function can be expressed as;

Total cost of catering services = (Cost per person*number of people, n) + Service charge

where;

Total cost of catering services=T

Cost per person=$15

Number of people=n

Service charge=$45

Replacing;

T = (15*n) + 45

T=15n+45

The second equation: T=15n+45, where n≥70