Shared groceries expenses between roommates to be divided as per specific consumption ratio and attendance
The solution to this problem is somewhat like grading on a curve. Use the consumption ratio multiplied by the attendance (which is also a ratio, out of 100 days) to calculate how much each person owes. This will leave you short. Then add together all of the shares in a category, determine the % increase required to get to the actual cost of that category, and increase all the shares by that %. Bren's comment is right on the mark.  The typical solution is to divide all bills by 5, and for special items, the person buying it just marks his name that it's not community food.  Your attempt at a granularity level this detailed is admirable, but produces false results. What happens when I claim to be a zero percent milk drinker but when someone gives me cookies, I have a glass of milk?  The effort to get true accuracy will cost far more in time spent than the results are worth. "For a personal finance forum, this is too complicated for sustained use and you should find a simpler solution. For a mathematical exercise, you are missing information required to do the split fairly.  You have to know who overlaps and when to know how to do the splits.   For an extreme example, take your dates given: Considering 100 days of calculation period,  If Roommate D was the only person present for the last 10 days, they should pay 100% of the grocery bill as they are the only one eating.   From your initial data set, you can't know who should be splitting the tab for any given day. To do this mathematically, you'd need:  But don't forget ""In Theory, Theory works.  In Practice, Practice works."" Good theory would say make a large, complicated spreadsheet as described above.   Good practice would be to split up the costs in a much, much simpler way." When I was in grad school (at an engineering school) my apartment-mates and I came up with this formula: Worked marvelously. "So your whole approach, and the attempt to scale this is flawed.  You will alienate roomates, provoke arguments, and make everyone's life more difficult.  There are too many variables and unforeseen possibilities.  For instance: ""Why should I have to pay for Joe to go buy the expensive organic milk when I'm fine with the cheap stuff?"" ""I planned on being here for 20 days, but was gone that long weekend, recalculate everything please."" ""I already paid for this month, but now you're asking for more because James wanted to recalculate for a long weekend?"" The right way to do this is to set up loose, reasonable agreement among the participants and treat that as a contract, but with some flexibility/mercy on small dollar amount items. For instance: There are 5 of us, so everyone provides food (and shops/cooks) one night a week.  We're solo on Friday and Saturday (people eat out more then anyway), and everyone puts in $10/week (or whatever) for breakfast cereal, snacks, etc.  If you can't be here on your night, work out to trade with someone.  If you miss out on a meal... oh well. As long as people feel like they have a say in the discussion generating this and it's not dictated to them, then most of the time this is far superior.  If people need this level of detail, then perhaps those people should live alone or move in with Sheldon Cooper from ""The Big Bang Theory""." I asked how often grocery purchases are made in a comment, but I'm going to assume weekly for simplicity. If a roommate is present during the week following a grocery purchase, then they owe a share according to their preferences as you outlined them above. You will have to track the grocery cost by category for that week and calculate the balance owed by the person for that week. If there is a partial week where most expect to leave for a holiday or otherwise, then fewer groceries should be purchased for that week, and the cost of shares will decrease accordingly. One need only indicate preferences once, and weekly attendance thereafter. The only issue remaining is to determine how to record shares. If a normal person consumes 3 shares of milk, and .5 shares of butter, and so on, you simply add up all of the milk shares for the week and divide the milk bill by those shares. Same with the butter. The downside of this method is that you have to predict consumption in advance, so you may instead calculate by consumption after the fact with a deposit paid by all to create the initial grocery supply which will be refunded when that person leaves the grocery purchase co-op, and shares are calculated by who participated in the week prior to the grocery purchase. This also allows for a mid-week refresh if any commodity incurs higher than expected consumption, with the mid-week bill being added to the end of week refresh trip.
"If you are living together 'casually' (no formal partnership agreement) then my option would be to ask her politely to as she has offered make a contribution  by buying the groceries or some such which you share. A 'voluntary contribution' not an enforceable one. Just as between flat mates where only one is the actual tenant of the flat but the tenancy allows 'sharing' . Check your tenancy allows you to share lodgings. PS An old Scots saying is ""never do business with close family"". I.e do not charge your wife or living in partner rent. It mixes emotional domestic life with a formal business life which can set feuds going in case of a break up or dispute. If you enter into child bearing relationship or parent hood or formal partnership or marriage then all this changes at some time in the future." "Seriously.  I can't tell you how many times I hear this scenario: Kid graduates college; kid runs out and signs lease on apartment ""because that's what you do""**; kid complains that he's in financial trouble and can't make ends meet.   Housemate sharing is most famously displayed in hit shows like Big Bang Theory or New Girl.  They get a much nicer place with better furnishings for way less money.  (However don't hook up with close neighbors or friends of other housemates, they do it for awkward laughs but it really results in awkward departure.)  It's more financially responsible.  It means the rest of your financial life will have more slack.  And when you move, obviously, it's no big deal, you just give all the notice you can, and go to the next town and find another housemate share.   ** I suspect a very significant factor is bringing home dates.  Well, there's nothing sexy about taking your date to McDonalds because you can't afford anything more.  See those shows... it works fine, you just have to be sensible about housemate choices.  Pick housemates who view things the same way, and who themselves are invested in making the shared space attractive, and aren't going to mind some ...activities... once in awhile." "People who rent an apartment will typically pay by check. Probably 90% of the checks I have written are for rent. To some extent this falls under the previously mentioned ""payments to another person"" rule." That's not really the point.  A small percentage of the 70% of the US population living within 150 miles will have disposable income to throw at marked up groceries.  Until someone can explain how this reduces overhead and lowers prices I'm just real skeptical.  Whole thing reeks of Webvan 2.0.  Walmart and Marc Lore are at least bringing creative ideas to the table.  The associate delivery for last leg is an interesting approach. I want to encourage diversity in means of producing goods so I organised subcategories by the means necessary to produce said goods, I organised categories by the same types of items that are all in a similar price range than each other, the randomiser will pick an item of the same category but of a different subcategory. (yogurt and cheese are in the same category, and same subcategory because the means of production is the same, so price change of one won't affect the economy as much) For example: Dinner together: DR Food          50 DR Spouse        50 CR Credit Card       100 For less than that you can get wings and nachos at a place on a college campus (so it isn't even cheap) and it will be more food than two people can possibly eat _and_ be really fucking good.  Now I want to go get nachos... My brother's wife does some pretty intense couponing. She recently posted on facebook when she bought about $300 worth of items for $30. It was almost all toiletries and food that her family uses regularly, though there were some items they've now got 3 months supply of. She told me that it is a pain to track and exploit all of the different coupons/discounts but the savings help to offset the cost of homeschooling 4 children. "Nobel laureate economist, Paul Krugman, wrote a piece many moons ago about economic expansion and money supply.  As an illustration of how money supply affects the economy, he used the example of a baby-sitting co-op.  While simplistic, it provides an easy to grasp notion of how printing money and restricting it (e.g. by pegging the currency to gold reserves) can affect the economy. Here is an excerpt from his webpage ( http://web.mit.edu/krugman/www/howfast.html ): ""With the decline of the traditional extended family, in which relatives were available to take care of children at need, many parents in the United States have sought alternative arrangements. A popular scheme is the baby-sitting coop, in which a group of parents agree to help each other out on a reciprocal basis, with each parent serving both as baby-sitter and baby-sittee. Any such coop requires rules that ensure that all members do their fair share. One natural answer, at least to people accustomed to a market economy, is to use some kind of token or marker system: parents ""earn"" tokens by babysitting, then in turn hand over these tokens when their own children are minded by others. For example, a recently formed coop in Western Massachusetts uses Popsicle sticks, each representing one hour of babysitting. When a new parent enters the coop, he or she receives an initial allocation of ten sticks.  This system is self-regulating, in the sense that it automatically ensures that over any length of time a parent will put in more or less the same amount of time that he or she receives. It turns out, however, that establishing such a token system is not enough to make a coop work properly. It is also necessary to get the number of tokens per member more or less right. To see why, suppose that there were very few tokens in circulation. Parents will want on average to hold some reserve of tokens - enough to deal with the possibility that they may want to go out a few times before they have a chance to babysit themselves and earn more tokens. Any individual parent can, of course, try to accumulate more tokens by babysitting more and going out less. But what happens if almost everyone is trying to accumulate tokens - as they will be if there are very few in circulation? One parent's decision to go out is another's opportunity to babysit. So if everyone in the coop is trying to add to his or her reserve of tokens, there will be very few opportunities to babysit. This in turn will make people even more reluctant to go out, and use up their precious token reserves; and the level of activity in the coop may decline to a disappointingly low level.  The solution to this problem is, of course, simply to issue more Popsicle sticks. But not too many - because an excess of popsicle sticks can pose an equally severe problem. Suppose that almost everyone in the coop has more sticks than they need; then they will be eager to go out, but reluctant to babysit. It will therefore become hard to find babysitters - and since opportunities to use popsicle sticks will become rare, people will become even less willing to spend time and effort earning them. Too many tokens in circulation, then, can be just as destructive as too few."" -- Paul Krugman, 1997 (accessed webpage 2010)." "One trick is to make all purchases end in a particular number of your choosing, say ""3"". From now on, all restaurant meals,gas purchases, and anything in your control, end them in 3. When you glance at the bill, you can skip these charges, and look carefully at the rest. It's not 100%, as you couldn't easily impact supermarket charges and many others, but it's half of my routine charges." I do online grocery shopping directly with my local supermarket.  Its great.   I keep a basic list of recipes/supplies I use pretty dependably every week.  I add them all at once.  Then I quickly pick through them to fine-tune and bam, done. 15 minutes while drinking mai tais in my underwear.   Schedule pickup for the next day on my way home from work. Agreed. I travel 8-10 weeks a year and usually my option for a private room in a shared home on airbnb is the same as a room at a mid-tier hotel. Whole house on airbnb is equivalent to a room at a higher tier hotel. I'll take the hotel 9 times out of 10 to get the points and because I know what I'm getting each time. My wife and I set up a shared bank account. We knew the monthly costs of the mortgage and estimated the cost of utilities. Each month, we transferred enough to cover these, plus about 20% so we could make an extra mortgage payment each year and build up an emergency fund, and did so using automatic transactions. Other shared expenses such as groceries, we handled on an ad-hoc basis, settling up every month or three. We initially just split everything 50-50 because we both earned roughly the same income. When that changed, we ended up going with a 60-40 split. We maintained our separate bank accounts, though this may have changed in the future. A system like this may work for you, or may at least provide a starting point for a discussion. And I do strongly advise having a frank and open discussion on these points. Dealing with money can be tricky in the bounds of a marriage. "If you or they feel uneasy about you simply paying more rent than them for equal usage, you can work out an agreement where they ""pay"" in other ways. For example, I once lived with someone that made about double what I did, and so he paid more rent than I did. In exchange, I was responsible for cleaning the kitchen. If your roommates hate cleaning then you could substitute something like running errands, cooking, or looking after plants/landscaping. If they have some specialized skills then they might be able to provide those instead (car maintenance, financial management, etc.). Of course you'll want to agree ahead of time on what the conditions of satisfaction for the task are, such as how often the kitchen will have to be cleaned and what the definition of ""clean"" is. You also can't be a jerk and make their job extra hard, such as by completely trashing the kitchen every night.  Obviously it will depend on the temperament of your roommates whether or not they'll be happy with this or feel insulted being ""the help"". It worked for us because it was a task he hated and one I didn't mind, and it kept me from feeling like I was mooching off him. I would feel them out when you propose a possible rent and utilities split. If they feel like it's an unfair burden on you, but they can't afford more, then you could suggest this as a way for everyone to contribute equally. Whatever you decide to do, don't hold it over their heads that you pay more. Agree on something that everyone feels is fair, whatever that is. If you want a concession due to paying more (such as you get the garage, get to pick the art on the walls, whatever), then agree to that up front. Then accept that you've made a fair deal and they don't owe you anything beyond what you've all agreed to. It's awful to feel like you live in someone else's home and that you are getting into ever deeper debt with a close friend or significant other, and it will breed resentment. If you can't do that, then don't share an apartment with them at all. The most important thing is that everyone feels it's fair, regardless of the numbers. If you cannot get to that agreement through dollars alone, you can have them contribute to the home in other ways, such as cleaning, cooking, or performing maintenance. Just make sure that everyone truly does feel it's fair and that you are all equals." "Completely linear?  We don't do that. Our daughter has a fixed allowance, and we expect a certain amount of help around the house as being part of the family.  We don't make any explicit ties between the two, and we don't seem to have any problems. We bought an eBay lot of Polly Pockets and divided them up into $5 bags.  (This is a better deal that what we could get in the store new.)  Her allowance isn't enough that she can ""buy"" one every week. After sensing her frustration we gave her the opportunity to earn some more money by doing extra work.  It happened to be cleaning up after our dogs in the back yard, a chore we had neglected for quite a while.  She stuck with the job, and truly earned that money.  (She'll be six in January.)  What's more, it was a good deal for me.  It needed to be done, and I didn't really want to do it. :) So, for now this seems like a fair balance.  It prevents her from getting the idea that she won't work unless she gets paid, but she also knows that working harder does have its rewards. We still have time to teach her the idea of working smarter. (This isn't a formal study.  It's just my experience.)"