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!

Answer 1

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

Answer 2

The answer is: 492, 455, 443, 430

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