Question

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 156 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 type will be in the complex.

Answer 1

x = one bedroom units

y = two bedroom units

z = three bedroom units

We know that:

x = 3 z ---> 1

y + z = x ---> 2

x + y + z = 156 ---> 3

Therefore combining 2 and 3:

2 x + 156

x = 78

from 1:

z = x / 3

z = 78/3

z = 26

from 2:

y = x – z

y = 78 – 26

y = 52

The summary of answers:

one bedroom (x) = 78

two bedroom (y) = 52

three bedroom (z) = 26