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.

number of 1 bedroom units are 96

number of 1 bedroom units are 64

number of 1 bedroom units are 32

Step-by-step 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