# 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. A family of 2 adults and 3 children go to the...

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.

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.

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)

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### 1 Answer

a) You need to write the cost function using the information provided by problem, that links the number of people and admission price such that:

`C(n) = 0.75*n + 5*3 + 8*2`

`C(n) = 0.75*n + 15 + 16`

`C(n) = 0.75*n + 31`

**Hence, evaluating the equation describing the cost of the familiy going to the fair yields `C(n) = 0.75*n + 31` .**

b) Notice that the domain of the function comprises the values of n that represents the number of raffle tickets bought. Hence, the number of the tickets bougth can not be negative. If there are no tickets bought, then n = 0.

**Hence, the domain of the function comprises the number of tickets bougth such that: `[0,oo).` **

c) The range of the function may be found substituting all values from domain for n in equation `C(n) = 0.75*n + 31` , hence for n = 0 => `C(0) = 31.75` .

**Hence, the interval `[31.75 , oo) ` expresses the range of the function.**