maths question

[sidewinder86]

4)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 two- bedroom apartments?
Any idea how to work this out ABers?
I thank you...

[tyrepill]

7(2 bed)+5 (1 bed)

[Gizmonster]

Let A = number of 1 bedroom appts.
Let B = number of 2 bedroom appts.

We have 2 equations and 2 unknowns:

A + B = 12 so A = 12 - B

and

(360 x A) + (450 x B) = 4950

substitute A = 12 - B

360 x (12 - B) + 450B = 4950

4320 - 360B + 450B = 4950

90B = 630

i.e. B = 7 (number of 2 bedroom appts)

and A = 5 (number of 1 bedroom appts)

A quick check:

(360 x 5) + ( 450 x 7)

1800 + 3150 = 4950 ...... which is correct so the answer you're looking for is 7

[sidewinder86]

Thank you tyrepill, but is there a mathematical formula for working this (and more complicated similar problems) out?

[sidewinder86]

thank you giz, cross posted there.

[TCL-MUMPING]

If you want to find out more about how to solve this type of problem, do a search for "simultaneous equation".

The general idea behind it is you have two or more unknown and a number of equations. You do a sum to eliminate an unknown and then substitute that answer for the unknown.

[TCL-MUMPING]

Sorry, that should have been "one or more unknown"

[dundurn]

Given the information given you there is another way of working out this sort of question.

Assume all the units are 1 bedroom. If so the monthly rental is 12 x �360 = �4320. In fact you get an additional �630. The difference between a 1 bedroom unit and a 2 bedroom unit is �90. To justify the additional �630, 7 of the units must be 2 bedroom.

[carsonking]

Dandurn, thats how i did it, lol, the other way went completly over my head.

[sidewinder86]

brilliant, thanks guys.