posted by Bowier4 .
A resturant offers a buffet dinner at group prices.It costs $10 for one person,$20 for two,$29 for three, $37 for four,$44 for five and so on.
A)how much does a buffet dinner for 8 cost?how much does a group of eight save if it's members eat together rather than alone.
B)the buffet costs the restaurant $6 per person.
How large a group can the restaurant serve without losing money?
P.S I came up with A.
Please and thank-you
Ok we have some kind of sequence that goes
10,20,29,37,44 for the first 5 terms.
It looks like the n-th term is given by
(1) n*10 -((n-2)(n-1))/2
At least this would be one expression to generate the sequence. I don't know if your text/teacher made you aware that through any finite set of data points there are an infinite number of functions. The expression (1) I gave would probably be the most 'natural' one we could use. To answer part A) put in 8 for n in (1) and calculate.
For part B) we know that the amount of revenue per group is given by (1). The cost is 6/person, thus use expression (1) - 6n = net profit. Since we want this greater than 0 set (1) - 6n => 0 and solve for n. Use the last n for which it is positive.
Hint: make a table and calculate n for the first dozen terms or so. I did not get twelve, so don't think this a short-cut.