A group of friends are going on a vacation together. They plan to rent a large house for $3000 and share the cost. They also estimate that the buying food for the week will cost $150 per person. Write a reciprocal function to calculate the cost per person for the trip (C), based on the number of people (P) who decided to come on the vacation. Explain how you came up with the function.
The cost for renting would be inversely proportional to the number of people attending,
that is,
the more people the less the cost.
However, the food cost is directly proportional to the number of people attending,
that is,
the more people the more the cost.
There is your explanation, now form the function.
To calculate the cost per person for the trip, we need to divide the total cost of the house and food by the number of people.
Let's call the total cost of the vacation (house + food) C and the number of people P.
The total cost of the vacation can be expressed as:
C = 3000 + (150 * P)
Now, to calculate the cost per person (C), we divide the total cost by the number of people (P):
C/P = (3000 + 150 * P) / P
The function to calculate the cost per person (C) based on the number of people (P) who decided to come on the vacation is:
C(P) = (3000 + 150 * P) / P
To calculate the cost per person for the trip, we need to divide the total cost by the number of people who decided to come on the vacation.
The total cost for the trip is the sum of the rental cost and the cost of food for the week. The rental cost is fixed at $3000 regardless of the number of people. The cost of food per person is $150, so the total cost of food is $150 multiplied by the number of people (P).
So, the function to calculate the cost per person (C) is:
C = (3000 + 150P) / P
We divided the total cost (3000 + 150P) by the number of people (P) to get the cost per person. The rental cost of $3000 is divided equally among all the people, and the cost of food per person ($150) is added on top of that.