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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?

Let x = number of 1-bedroom units and y = 2-bedroom units. Then, when all the units are rented

x + y = 12

and

x(360) + y(450) = 4950.

Substitute for x in terms of y -> x = 12-y

(12-y)(360) + y(450) = 4950.

Solving for y,

12(360)-y(360) + y(450) = 4950 -> y(450-360) = 4950-12(360) or y(90) = 630

y = 630/90 = 7 and x = 5.

Plugging these back in gives the right answer.

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