Question

An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for $360 and $450 per month, respectively. when all units are rented, the total monthly rental is $4,950. what is the number of twobedroom apartments?

Answer 1

x = one bedroom apts and y = 2 bedroom apts

x + y = 12.....x = 12 - y
360x + 450y = 4950

360(12 - y) + 450y = 4950
4320 - 360y + 450y = 4950
-360y + 450y = 4950 - 4320
90y = 630
y = 630/90
y = 7...so there are 7 two bedroom apts <==

Answer 2

The number of two-bedroom apartments are:

7

Explanation:

Let the number of one-bedroom apartments be: x

and the number of two-bedroom apartments be: y

Now, it is given that:

An apartment building contains 12 units .

This means that:

x+y=12--------------(1)

and the cost of one-bedroom apartment=$ 360

and cost of two-bedroom apartment=$ 450

The total monthly rental is $4,950.

i.e. 360x+450y=4950------------(2)

From equation (1) we have:

x=12-y

on putting the value of x in terms of y in equation (2) we have:

360(12-y)+450y=4950

i.e.

360×12-360y+450y=4950

i.e.

4320+90y=4950

i.e.

90y=4950-4320

i.e.

90y=630

i.e.

y=7

Number of two-bedroom apartments = 7

and number of one-bedroom apartment= 5 (12-7=5)