Apartment Word Problem

In an apartment building some apartments have a one bedroom and the rest have two bedrooms if there are a total of 50 apartments and 80 bedrooms how many apartments have one bedroom and how many have two bedrooms.

Solution.

Let x be the number of apartment with 1 bedroom

Let y be the number of apartment with 2 bedrooms

We then derive the following 2 equations from the problem.

x + y = 50 (1)

x + 2y = 80 (2)


Use equation (1) to solve for x

x + y = 50

x + y - y = 50 - y

x = 50 - y

Replace x into equation (2)


50 - y + 2y = 80

50 + y = 80

50 - 50 + y = 80 - 50

y = 30


x = 50 - y = 50 - 30 = 20

Therefore, 30 apartments have 2 bedrooms and 20 apartments have 1 bedroom.