Chapter 10.5, Problem 32MS

Roomate wrangling. You and a friend rent a two-bedroom apartment together. The rent is $1000 per month. One bedroom is nicer than the other, so you want to adjust the rent fairly. The table below shows the maximum rent each of you is willing to pay for each bedroom.

Before deciding on actual rents, is it clear who should get the small bedroom and who should get the large bedroom? Why or why not? To determine a possible way to split the rent, plot the points $\left(\text{300,700}\right)\text{, }\left(\text{400,700}\right)\text{, }\left(\text{300,600}\right)\text{, and }\left(\text{400,700}\right)$ on a pair of xy-axes. (What do the x and y coordinates represent?) Use two line segments to connect the points in an X shape. Estimate the coordinates of the point where the line segments intersect. Do these coordinates seem reasonable as rents for the two bedrooms? Which person gets which room?