How many two bedroom apartments are there?

Question

An apartment building has 12 units. One and two bedrooms available at $360 and $450 respectively. When all units are rented the total is $4950. How many two bedroom apartments are there?

Answer 1

We'll call all of the one bedroom apartments x, and all of the two bedroom apartments y. If you add all of the one bedrooms and two bedrooms together, you have 12 apartments:

 

x + y = 12

 

If you rent a 1 bedroom for $360 and a 2 bedroom for $450, when you are at full occupancy, you get $4950:

 

360x + 450y = 4950

 

So you have two unknowns and two equations. Since the number of unknowns matches the number of equations, you can now solve:

 

x + y = 12 -----> x = 12 - y

 

360x + 450y = 4950

360(12 - y) + 450y = 4950 (plugged in what x was solved for two lines above)

4320 - 360y +450y = 4950

4320 + 90y = 4950

90y = 630

y = 7

 

Now plug this answer back into x equation:

x = 12 - 7 = 5

 

So there are 5 one bedroom apartments and 7 two bedroom apartments.

Answer 2

Hi Pamela.

 

This is a classic system of equations problem. You have two unknowns (how many one bedroom apartments and how many two bedroom apartments there are) although at the end of the day you only care about 1 of them. The fact you only want to know how many two bedroom apartments there are will tell you which variable to eliminate and which variable to solve for, saving you some work at the end of the day.

 

First let's come up with some variables. I'm going to say that:

 

S = # of one-bedroom apartments (S for single just make it easier to track)

D = # of two-bedroom apartments (D for double)

 

You have a grand total of 12 units. That means the number of singles and the number of doubles adds up to 12.

 

S + D = 12

 

Singles cost $360 a month, doubles cost $450 a month. When everything is rented the land lord makes $4950 a month. So, $360 a month times the number of singles PLUS $450 a month times the number of doubles equals $4950.

 

360*S + 450*D = 4950

 

Now you have two equations, two unknowns.

 

S + D = 12

360S + 450D = 4950

 

You care only about the number of doubles, meaning you should eliminate S. I'm going to multiply the top row by -360.

 

-360S - 360D = -4320

360S + 450D = 4950

 

Add the two equations.

 

90D = 630

 

D = 7

 

There are 7 two-bedrooms in this apartment building.

 

Hope this helps.

 

Follow-up: is this a real apartment complex? If so I would LOVE to know where it is I can find these rates.