Write a function in the form of C(n) to describe the cost of this family going to the county fair.   2a) Write a function in the form of C(n) to describe the cost of this family going to the county fair. (2 pts) 2b) What is the domain of this function? (1 pt) 2c) What is the range of this function? (1 pt) 2d) If the family wants to spend at most $35, what is the maximum number of raffle tickets that they can buy? You must write the inequality equation to get full credit (2 pts)

Expert Answers

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a)  Multiply the cost of each item, admission or raffle tickets, by the number of items purchased.

      Admission=2 adults * cost per adult + 3 children * cost per child

      2(8) + 3(5) = 16 + 15 = $31 is the cost of admission

      Total spent on raffle tickets=cost per ticket*number of tickets

     Number of raffle tickets purchased is unknown, so let n = number   of tickets purchased.


    Total cost at the county fair = Admission + Raffle Tickets

        Therefore,   C(n) = 31 + 0.75 n


b)  Domain is all "acceptable" values for n.  n >0 because the family will purchase 0 or more raffle tickets, but never a negative number of tickets.

c)  To find the range substitute the lowest value from the domain (0) into the function.  This is the lowest range value and they will increase from that value.  So C(0) = 31 + 0.75(0) = 31.75.  Your range is C(n) >31.75

d)  Since the family spends "at most $35", 35 is the maximum total value.  Therefore, the total spent is less than or equal to $35.

     Your inequality is:   31 + 0.75n <35

      If you are supposed to take into account that n >0 (no purchase of negative tickets), you would want a compound inequality.  I don't know if you have studied those yet or not.  If the following inequality doesn't look familiar to something you have seen in class, simply ignore it and use the previous one.

        31 <31 + 0.75n <35

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