# Math geeks: Pop quiz, can you help with this rent money problem?

Asked by gambitking (4201) January 30th, 2012

Here’s a math problem I’m having trouble with: Four roomates: John, Jim, Jack and Jill are trying to pay rent, which includes some variables.

Jack and Jill are a couple, they pay 40% of the rent. They also pay \$20 of the amount for a parking spot. Jim and John pay 30% of the total rent each. But Jim has a discount on the rent… he’s a student, which earns a 5% off the total rent. But he calculates the dollar amount of that discount, and takes that dollar amount off his portion of rent. The total rent is \$1282.80.

Who pays what?

(PS: It’d be cool if you can show how you reached the answer)

Observing members: 0 Composing members: 0

You asked a question about the roomie with the discount a while ago. I asked you to provide an update….

jca (36043)

That’s a weird amount for rent.

jca (36043)

Yeah now we’re just all trying to figure out who pays what , given all the variables. Its head-wracking

gambitking (4201)

I don’t get “they also pay \$20 of the amount toward a parking space.” \$20 of what amount? You mean \$20 of their total goes toward a parking space? You worded it in a way that makes it unclear.

jca (36043)

There are two confusing bits to the question. First, is the amount for parking separate? If so, then we can discount it for the purposes of the current problem. Second, is \$1282.80 the total amount due before or after the discount?

SavoirFaire (26543)

Assuming that the parking amount is separate and \$1282.80 is the amount due after the discount, then we know the following:

`(Jack and Jill’s share) + (John’s share) + (Jim’s share) + (Discount) = \$1282.80 + (Discount)`

Now, let x = 1% of the pre-discount rent. That allows us to say the following:

`40x + 30x + 25x + 5x = \$1282.80 + 5x`

We can then subtract 5x from each side and combine the coefficients on the left side to get:

`95x = \$1282.80`

From this we can conclude that:

`x = \$13.50315 (rounded)`

Jack and Jill’s share is 40x, which is equal to \$540.126. Round this up to \$540.13. John’s share is 30x, which is equal to \$405.094. Round this down to \$405.09. Jim’s share is 25x, which is equal to \$337.578. Round this up to \$337.58.

`\$540.13 + \$405.09 + \$337.58 = \$1282.80`

Voilà!

SavoirFaire (26543)

So the total rent is \$1282.80? Jim is taking the 5% discount off the \$1282.80 out of his 30% of the rent? I did it differently than @SavoirFaire and came up with different amounts. I think we got different amounts because we handled the 5% discount differently (he did it as \$1282.80 being the rent after the discount and I did it as being the total rent before the discount). I left the parking thing out of it because I wasn’t sure how that really fit in.

If that’s the case, 5% of \$1282.80 (\$1282.80 * .05) is \$64.14. So that is the amount Jim would be taking from his portion of the rent if I’m reading this correctly. John and Jim each pay 30% of the total rent, so they would pay \$384.84 (\$1282.80 * .30) each, with Jim then taking the \$64.14 from that to make his portion \$320.70.

Jack and Jill pay the remaining 40% of the rent which is \$513.12 (\$1282.80 * .40).

Totalin up the \$320.70 (Jim’s part) + \$64.14 (the 5% discount that Jim gets credit for) and \$384.84 (John’s part), and the \$513.12 (Jack and Jill’s part) = \$1282.80

Seaofclouds (23082)

Assuming that the parking amount is separate and \$1282.80 is the amount due before the discount, then we know the following:

`(Jack and Jill’s share) + (John’s share) + (Jim’s pre-discount share) = \$1282.80`

Again, let x = 1% of the total (pre-discount) rent. That allows us to say the following:

`40x + 30x + 30x = \$1282.80`

We can then combine the coefficients on the left side to get:

`100x = \$1282.80`

From this we can conclude that:

`x = \$12.828`

Jack and Jill’s share is 40x, which is equal to \$513.12. John’s share and Jim’s (pre-discount) share are each 30x, which is equal to \$384.84.

`\$513.12 + \$384.84 + \$384.84 = \$1282.80`

But now we have to figure out what Jim’s actual payment is. For this we take his payment and remove 5%. So if we let y = Jim’s actual payment:

`y = \$384.84 – (\$384.84 * 0.05)`

This reduces to:

@y = \$384.84 – \$19.242

Or further:

`y = 365.598`

Jim’s actual payment, then, will be \$365.60 when rounded to the nearest penny. Note that it does not matter in this case if we round at the end or in the second to last step. If we had rounded the discount to \$19.24, the amount owed would still have come out to \$365.60.

SavoirFaire (26543)

Oh, and @Seaofclouds makes a good point. It matters whether or not the discount is taken off the top or not. This is another detail we would need to know before deciding which method of calculating applies to the particular situation.

SavoirFaire (26543)

@SavoirFaire I read it as Jim was going to take all of the discount off his portion of the rent and the details say that the 5% dicount comes off the total rent, not just his portion of the rent. Hopefully @gambitking will come back and explain it a bit better.

Seaofclouds (23082)

@Seaofclouds I think your reading of the question is perfectly reasonable. I would have given a calculation for that version of the problem, but you beat me to it. I suppose it depends in part on how we understand the qualification that Jim “calculates the dollar amount of that discount, and takes that dollar amount off his portion of rent.”

SavoirFaire (26543)

You’re kidding, right?

MollyMcGuire (7725)

@Seaofclouds and @SavoirFaire: @gambitking asked a question about how the rent discount should be applied (I believe he worded it and you can search for “How should a special rent discount be applied among roomies?”), where the discount was discussed and various people weighed in as to how it should be applied. I posted one of my “please provide an update as to how this worked out” or something like that, and @gambitking didn’t respond. That’s why the first answer to this question above is me reminding @gambitking to provide an update with the details.

jca (36043)

Not sure how I didn’t specify enough in my question about the 5% discount. Here’s the key point regarding that:

“He’s a student, which earns 5% off the total rent. But he calculates the dollar amount of that discount, and takes that dollar amount off his portion of rent.”

Thought that was pretty clear, what is the misunderstanding?

I think @SavoirFaire got the closest…. its easy to forget to apply that 5% off the total rent !! (so the final total we actually pay is closer to \$1221 total). Also, it’s easy to make the mistake of keeping the \$20 parking as part of the calculation when applying that 5%, meaning that Jack n Jill’s parking cost was improperly discounted by 5%, giving them an extra \$1.00 they shouldn’t have.

@ica – jeez sorry about not providing an update already. you sure seem to be concerned about that. I’m not used to following up on things like this after a long period of time. will you ever forgive me???

gambitking (4201)

@gambitking Taking the discount off the total rent and giving Jim credit for it from his 30% is how I did it in my calculations. @SavoirFaire did it two ways that were different from that (one thinking the \$1282.80 was after the discount and one with only taking 5% off Jim’s portion of the rent, not the total rent).

Seaofclouds (23082)

@gambitking: LOL! The only reason I remembered this was that it was only the other day I was scrolling down my list of New Activity and came across the other question. I was not so curious as to the specifics, but more curious about if everyone agreed on it all. I know when there are four people with four different opinions, there is potential for problems. I just posted the request to follow up the other day.

You are forgiven! The Update Lady likes her updates! That’s her job!

jca (36043)

@ica , haha, yeah I wondered if anyone would relate the two, so thanks for paying attention!

I wouldn’t say we all “agree” ... its more like “tolerate” ... but of course the guy that’s getting an extra \$720 back this year by leveraging his roomies’ purchasing power isn’t disagreeing, that’s for sure.

gambitking (4201)

Yes, I agree that @Seaofclouds’ calculations are correct given the clarifications. The amounts paid should be:

Jack and Jill – \$513.12
John – \$384.84
Jim – \$320.70

SavoirFaire (26543)