M119 Project #1 – The Divorcee Problem (rev B 8/09)

Date due: 25 points – 5 pt penalty for each class late

Objective: Linear Function and Intersection of Functions

After five years of marriage, a couple decided to divorce and had to sell their home. They lived in a very lovely home which they had purchased together, but the lady had contributed an extra $20,000 toward the down payment. The current asking price is $149,500. The realtor’s fee is 7% of the selling price. The pay-off amount due to the Mortgage Company is $85,483. There are additional closing costs of $2784 for taxes and $250 for a title search.

The woman suggested that when the house was sold, closing cost and realtor paid, she should receive the first $20,000 and then the remainder of the money would be divided 50%/50% (Method A). The man had a counter proposal of 80% of the profit to the woman and 20% of the profit for himself, because the woman had contributed 80% of the down payment and the man had contributed 20% of the down payment (Method B).

I. (5 pts) If the couple received a $130,000 offer on the home,

a. Find the profit for each person for each method. Show your work

	Man	Woman
Method A
Method B

b. If the selling price is $130,000 which method is to the woman’s advantage?

Which method would most benefit the man?

II. (5 pts) If the couple received a $135,000 offer on the home,

a. Find the profit for each person for each method. Show your work.

	Man	Woman
Method A
Method B

b. If the selling price is $135,000, which method is to the woman’s advantage?

Which method would most benefit the man?

III. (15 pts) If the woman is your friend, and no offer has yet been made, help her to determine the

selling price which would enable her to profit by accepting is 80%/20% option –

thereby appearing very agreeable to his suggestion!

a. Set up a function to find the woman’s profit in terms of selling cost if Method A is used.

b. Set up a function to find the woman’s profit in terms of selling cost if Method B is used.

c. Use algebra and verify with a graph to find what selling price

makes the woman’s profit the same by either method.

What is the selling price at that point?

d. What would be the man’s profit and the woman’s profit at that point?