calculate how my rent should increase

Question

I have 5 roommates and we pay rent based on the quality of room. Here's the current breakdown:

400 370 360 350 340 Total: 1820

We are losing a roommate and the person in the last room is moving into their old room. However rent stays the same so the new breakdown is:

400 370 360 350

As you can see this results in an additional $340 that has to be allotted to each roommate to equal the 1820.

My question is how much should everyone's rent increase while keeping the correct proportions?

Thanks!

As one room is presumably empty, do you want to ignore it's "quality" while new division of prices is done or do you want to take that room's "quality" into consideration too? — Shraddheya Shendre, Nov 25 '16 at 22:27
@ShraddheyaShendre that room is being vacated and thus instead of having 5 roommates paying 1820, its 4 roommates still paying 1820 and that last room is empty and not accounted for — sparkles, Nov 25 '16 at 22:33

score 1 · Answer 1 · answered Nov 25 '16 at 22:39

1

The answer is: 492, 455, 443, 430

However, please don't use stackexchange as a calculator.

answered Nov 25 '16 at 22:39

cubeception

thank you! can you show me the math of how you got to this answer? – sparkles Nov 25 '16 at 22:42
@sparkles see my answer – Brandon Nov 25 '16 at 22:46

score 0 · Accepted Answer · answered Nov 25 '16 at 22:45

Why not just compute the proportion of the rent for each person..And then when you have all those proportions, just multiply each by 340?

For example, we know the initial breakdown is 400 370 360 350 340

 a = 400/1820 = .22
 b = 370/1820 = .20
 c = 360/1820 = .20
 d = 350/1820 = .19
 e = 340/1820 = .19

Please note I did round the initial percentages, so there may be some slight dollar differences, but very small

Then we will get rid of e, and split this proportion up into the 4 remaining people.

Such as $19/4$ = $4.75$ to each person.

Thus the new proportions would be

 a = 26.75%
 b = 24.75%
 c = 24.75%
 d = 23.75%
 = 100%

Now just multiply $340$ by each proportion

 a = 340*.2675 = 90.95
 b = 340*.2475 = 84.15
 c = 340*.2475 = 84.15
 d = 340*.2375 = 80.75

Finally,

personA = 400 + 90.95 = 490.95
personB = 370 + 84.15 = 454.15
personC = 360 + 84.15 = 444.15
personD = 350 + 80.75 = 430.75
= 1820

@sparkles The reason for the down votes is because people like to see a users first attempt. I understand that sometimes you might not even know the first step in solving a problem. That's why I didn't just provide an answer to your question, but also steps on how to go about this questions and possibly similar questions in the future. — Brandon, Nov 25 '16 at 22:59
that's exactly what i wanted to see, the work to getting the answer. because i had no idea how to approach it lol — sparkles, Nov 25 '16 at 23:02

2 Answers2