Question

Cantwell Associates, a real estate devel- oper,is planning to

build a new apartment complex con- sisting ofone-bedroomunits and
two- and three-bedroom townhouses. A total of192 units is planned,
and the number of family units (two- andthree-bedroom town- houses)
will equal the number of one-bedroomunits. If the number of
one-bedroom units will be three times thenumber of three-bedroom
units, find how many units of each typewill be in the complex.

Answer 1

number of 1 bedroom units are 96

number of 1 bedroom units are 64

number of 1 bedroom units are 32

Explanation:

Let the number of 1 bedroom units be 'a'

number of 2 bedroom units be 'b'

and,

number of 3 bedroom units be 'c'

now,

according to the question

a + b + c = 192 ................. (1)

also,

b + c = a ..............(2)

and,

a = 3c ...................(3)

now,

substituting value of 'a' from 3 into 2, we get

b + c = 3c

or

b = 2c ...................(4)

also,

from 3 and 1

3c + b + c = 192

or

4c + b = 192 ................(5)

now from 4 and 5,

4c + 2c = 192

or

6c = 192

or

c = 32 units

now, substituting c in equation 4, we get

b = 2 × 32 = 64 units

and, substituting c in equation (3), we get

a = 3 × 32 = 96 units

Therefore,

number of 1 bedroom units are 96

number of 1 bedroom units are 64

number of 1 bedroom units are 32