Algebra assessment

Question

A youth group is planning a trip to a local amusement park. They are taking a van which holds 10 people. It will cost $25 for parking and tickets to enter the park are $18 per person. 

1. 1. Finding the domain for the situation: (5 points each)
2. a. What is/are the constraint(s) for this situation? Explain
3. 
   
4. b. What is the domain of the function?
5.  
6. 2. Finding the range for the situation above: (5 points each)
7. a. What are the costs for the smallest number of people and largest number of people? Explain your reasoning for both answers.b. What is the range of the function?
8.  
9. 3. Create an equation for this situation. Make sure you explain what your variables represent. (10 points)

Answer 1

C = 25(v) + 18(p)

C=cost measured in dollars, v= number of vans, p= number of people, v and p are limited to integers

domain is all integers, 0 to infinity for v and p

unless v is limited to 0 or 1

then domain for p is limited to 0, 1,2,3,4,5,6,7,8,9, or 10

range is 0 to infinity

Unless v is limited to 0 and 1

then range is 0, 43, 61, 79, 97, 115, 133, 151, 169, 187, or 205

Cost for 10 people is 25+18(10) = $205

Cost for 0 people is $0

Cost for 1 person is 25+18= $43

or you could make 1 person just walk, or just drop him off & pick him up later, and then the lowest cost is $18

So, lowest cost is either $0, $18, or $43. The problem probably wants $43 for the lowest cost answer though. That's not counting cost of gasoline, and depreciation on the van or possible salary for the driver and any possible traffic tickets and fines, maybe a flat tire and cost of a new tire. Maybe cost of a new van or higher insurance premiums after a major accident, and hospital costs & the ambulance.