1. Cantwell Associates, a real estate developer, is planning to build a new apar

Question

1. Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units, and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each tpe will be in the complex.

a)Fill in the following table with the appropriate coefficient for each variable in each of the equations.

b) Rewrite the above system of 3 equations as a matrix equations:

x (number 1 bedroom units) y (number 2-bedroom units) z (number 3-bedroom units) Totals Total number of units Relationship between 1-,2-and 3-bedroom units Relationship between 1- and 3- bedroom units

Explanation / Answer

Let

X= 1 bedroom unit

Y=2 bedroom unit

Z=3 bedroom unit

Given X=Y+Z

X=3Z

By solving these 2 we get

3Z=Y+Z

2Z=Y

Given that total X+Y+Z=192

3Z+2Z+Z=192

6Z=192

Z=32

y=2Z=64

X=3z=96

Relationship between X:Y:Z=3z:2z:z=3:2:1

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