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balu736 [363]
3 years ago
8

A restaurant offers a catering service which costs $25.00 per person with a $119.50 service charge. For parties of 50 or more pe

ople, 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.
Mathematics
1 answer:
Molodets [167]3 years ago
7 0

Answer:

T1(n) = 25n +119.50  where n belongs to 1 \leq n.

T2(n) = 20n + 59 where n belongs to 50\leq  n.

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 1 \leq n

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 50\leq  n.

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

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So, we know the sum of the first 17 terms is -170, thus S₁₇ = -170, and we also know the first term is 2, well

\bf \textit{ sum of a finite arithmetic sequence}\\\\
S_n=\cfrac{n(a_1+a_n)}{2}\qquad 
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----------\\
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\end{cases}
\\\\\\
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\\\\\\
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well, since the 17th term is that much, let's check what "d" is then anyway,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
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d=\textit{common difference}\\
----------\\
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a_{17}=-22\\
a_1=2
\end{cases}
\\\\\\
-22=2+(17-1)d\implies -22=2+16d\implies -24=16d
\\\\\\
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========================================================

Part (1):
=======

<span>The distance between the lines
</span>
<span> Y₁ = 3x + 10    and       Y₂ = 3x - 20</span>
∴ m = 3  , c₁ = 10  and  c₂ = -20
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========================================================

Part (2):
=======

<span>The distance between the lines
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