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...

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)

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schwangmath's profile pic

schwangmath | High School Teacher | (Level 1) Adjunct Educator

Posted on

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.

       0.75n 

    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

horseslover004's profile pic

horseslover004 | Student, Grade 9 | (Level 2) eNoter

Posted on

Sorry Guys but i forgot to put the problem in it is A family of 2 adults and 3 children go to the county fair that sells raffle tickets for 75¢ each. Admission price is $5 per child and $8 per adult. Let n be the number of raffle tickets bought. :) sorry

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