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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?

Hello Angelo
Please find below the approach and answer to this problem:

Let us assume that there are x number of one-bed apartments and y number of two-bed apartments in the building.

Since total number apartments are 12, we get,
x + y = 12  ---------------------------- (1)

Now, rent of one-bed apartment is $360. Thus, total rental for one bed apartments is x*360 (=360x)
Similarly, rent of two-bed apartment is $450. Thus, total rental for two bed apartments is y*450 (=450y)

Thus, total rental for all apartments is = 360x + 450y
T\However total rental is given as $4,950.

360x + 450y = 4,950

Dividing both sides by 90, we get,
4x + 5y = 55 ------------------------- (2)

From equation (1) above, we get,
y = 12 - x -------------------------(3)

Replacing value of y (12 - x) from equation (3) into equation (2) above, we get

4x + 5(12 - x) = 55
4x + 60 - 5x = 55    (after expanding the bracket)

-x + 60 = 55
-x = -5
x = 5  -------------------------------- (4)

Putting x = 5 in equation (3) above, we get
y = 12 - 5 = 7 --------------------(5)

As we are assumed that there are y number of two bed apartments, we conclude from (5) above that there are total 7 two bed apartments in the building.

I hope that this helps. Please let me know should you know further clarification.

All the best!


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Pawan Musale


I can answer questions wrapped in words. This includes questions related to Logic, Natural Numbers, Integers, Real Numbers, Complex Numbers, Number Theory, Geometry, Trigonometry, Graph Theory, Square Roots, Basic Integration, Profit-Loss problems, Work-Time problems, Equations etc.


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