Math Journal: Bedroom arithmetic

New building projects in Bloomington can be controversial, especially when the proposed new apartments are marketed to students at Indiana University. Typical for such projects are higher numbers of bedrooms for each apartment.

CDG Development Motel 6 site
A rendering of Collegiate Development Group’s proposed project on North Walnut Street viewed from the southwest.

A recently proposed 820-bedroom housing development on North Walnut, at the current Motel 6 site, prompted this comment from one city councilmember about the number of four-bedroom units in the proposal (compared with other, smaller apartments):

“All I can say is, Wow!”

Collegiate Development Group’s proposal will be in front of Bloomington’s city council for a first reading on Wednesday, July 31, 2019. In mid-June the city’s plan commission voted unanimously in favor of the site plan.

The city council will be weighing whether to change the zoning of the land to a “planned unit development” (PUD)—so that the density of the property can exceed the normally allowed 15 “units” per acre. The area of the land for the proposed project totals 3.85 acres.

To calculate the project’s density—that is, the number of units per acre—the first step is to calculate the number of “units.” It’s not as simple as counting up the individual apartments. A four-bedroom apartment is in some sense a “unit,” but doesn’t count the same as a one-bedroom apartment.

The City of Bloomington uses the following weighting scheme to define “dwelling unit equivalents” (DUEs):

1 five-bedroom apartment = 2 DUE
1 four-bedroom apartment = 1.5 DUE
1 three-bedroom apartment = 1 DUE
1 two-bedroom apartment = 0.66 DUE
1 one-bedroom apartment = 0.25 DUE
1 micro-studio apartment = 0.2 DUE

It’s common for people to talk about how much denser a project is than the normally allowed 15 units per acre.

Feel free leave your answer to the problem below as a comment. If The Beacon has set up the commenting system correctly, your correct answer won’t spoil things for other people, because it will sit unseen, until it gets “approved.” After a month or so, any comments with correct answers will be approved. (If this website manages to turn a buck or two, maybe correct answers to future real-world math problems from The Beacon’s Math Journal will be rewarded with some kind of prize. But it’s not there, yet.)

Dwelling Unit Problem (CDG’s PUD Proposal at Motel 6 Site)

For a planned unit development, Collegiate Development Group has proposed the following mix of apartment unit sizes:

0 five-bedroom apartments
158 four-bedroom apartments
0 three-bedrooms apartments
76 two-bedrooms apartments
2 one-bedrooms apartments
34 micro-studios apartments

Using Bloomington’s DUE weighting scheme, calculate the density of the project expressed in terms of DUEs/acre. (Show your work!)

One thought on “Math Journal: Bedroom arithmetic

  1. 76.483116 dues per acre. 4 bedrooms + 237 dues, 2 bedrooms 50.16 dues, one bedroom= .50 dues, micro-studios = 6.8 dues. Total dues 294.45 dues divided by 3.85 acres = 76.48 etc.

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