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11 July, 04:05

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.

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  1. 11 July, 04:34
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    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
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