what fraction of the bill should each person pay?

Question

Sonya is a student at Urban State College. Because her financial resources are limited, she has moved into a house with four other people. The house is high speed internet, and the bill comes every two months. Sonya moved in on August 1. When the bill for July-August comes, what fraction of the bill should each person pay?

Answer 1

Firstly, we have to realize that the bill will be accounted for 2 months: July and August. Also, we know that 4 people lived in the house in July and then 5 lived in the house in August after Sonya moved in. We need this information so that we can calculate how much total internet was used over those two months. To calculate it, we an add 4 person-months. One person-month means one person using the internet for one month. Since it was 4 person-months in July and 5 person-months in August, we can add these up which gives us a total of 9 person-months.

Let B be the internet bill of July to August. We know that since Sony lived in the house only in August, she contributed 1 person-months out of the total nine. So she owes 1/9 of the bill (1/9B). Each of the other housemates lived in the house during both July and August, giving each of two-person months of usage. Therefore, each of them would pay 2/9 of the bill (2/9B).

So, Sonya pays one-ninth of the bill (1/9 B) while each of the four other housemaths pays two-ninths (2/9 B).

Answer 2

Assuming a fair division of bills, Sonya will only have to pay for the service for August and not for July's cost.

-Given the total bill, totalX, divide by 2 to get the cost for August. totalX/2 = augustX

-Then divide by the 5 people to get Sonya's fraction augustX/5 = sonyaX

-Everyone else will be divide the remainder (totalX - sonyaX)/4