Question

Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of x one-bedroom units, y two-bedroom townhouses, and z three-bedroom townhouses. A total of 186 units are 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

The x one bedroom is 93 unit, y two-bedroom is 62 units, and z three-bedroom is 31 units.

Explanation:

Consider the provided information.

A total of 186 units are planned,

Apartment complex consisting of x one-bedroom units, y two-bedroom townhouses, and z three-bedroom townhouses.

This can be written as:

`x + y + z = 186` ......(1)

The number of family units (two- and three-bedroom townhouses) will equal the number of one-bedroom units.

`x = y+z` ......(2)

The number of one-bedroom units will be 3 times the number of three-bedroom units,

`x = 3z` ......(3)

From 3 and 2.

`3z-z=y`

`2z=y`

Substitute the value of x and y in equation 1.

`3z+ 2z + z = 186`

`6z= 186`

`z= 31`

Substitute the value of z in equation 3

`x = 3(31)`

`x =93`

Substitute the value of z in
`2z=y`

`2(31)=y`

`62=y`

Thus, the x one bedroom is 93 unit, y two-bedroom is 62 units, and z three-bedroom is 31 units.