# Math Help - tried to use problem solving process for my problem

1. ## tried to use problem solving process for my problem

Hi guys. This might be a simple problem for you but at themoment I can’t get my head a round it. I tried using the problem solving process re sticky thread to no avail. Would greatly appreciate your input.

Three parties have 1/3 liability under an incorporation.They are required to contribute $1000 each to a sinking fund. Two partiescontribute the full amount,$1000 each. The other party provides services tothe incorporation, totalling $600, as a separate entity to the corporation. That party also forwards payment of$400 believingthe value of their services should be accepted in lieu of outstandingcontribution (1000-400=600)
I’m wanting an opinion and mathematical explanation/exampleif that is acceptable or not. My thoughts are, as the party providing theservice was not part of the incorporation all three members are equally liablefor 1/3 of the $600. If we accept their contribution of$400 they would still owe$200 to the incorporation as their share of the$600 expenses for services.

2. ## Re: tried to use problem solving process for my problem

This really isn't a math question - it seems more like an accounting question. But I'll try:

If the original aim of the sinking fund is to have a pool of $3K that can be used by the corporation, and if each partner is contributing an equal amount, then each partnet must contribute$1000. Now if one person wants to contribute $400 cash +$600 in services that would be OK only if the $600 donation of services is truly a savings to the corporation. In other words by contributing$600 in services (washing windows or whatever) does the corporation save $600 in cash expenditures that it otherwise would have had to pay? If so - then the corp could accept the$600 in services and transfer $600 out of the expense budget and into the sinking fund. End result is the sinking fund has the$3K in cash it needs, and the expense budget took a $600 hit for expenses it was planning on anyways. 3. ## Re: tried to use problem solving process for my problem Hi ebaines and thanks for the reply. You are correct, of an accounting nature but wanted to see how the distribution of expense would be shown mathematically. Possibly irrelevant but the services were of a capital nature so drawn from the sinking fund. Just clarifying. The services were not a donation in lieu off. The member took over an existing "contract", if you like, as he now lives there. All three members including that member are equally responsible for one third. Simply, why pay someone else if a member can benefit. I would have thought the portion that represents the contribution to the sinking fund from the member providing the service would be two thirds of$600, being a figure of $400 towards their contribution to the$1000 sinking fund resulting in them only contributing $800 in total. 4. ## Re: tried to use problem solving process for my problem I'm not following what yuo mean by: "All three members including that member are equally responsible for one third. Simply, why pay someone else if a member can benefit." I thought all three members are equally responsible for the entire fund, which is equivalent to saying that each individual member is responsible for one third. No? And I don't understand how the services were not in lieu of a cash contribution - I though that was the point? Perhaps if you provided more details on how this fund was set up, what services were provided by the member, and how those services are valued it would help make it clearer. 5. ## Re: tried to use problem solving process for my problem Originally an external contractor mowed the common property lawns for$750. All members were liable for $250 each. One of the members said he could do it cheaper at$600 and bill the corporation for $600. There was no agreement the amount of$600 was to be considered as being in lieu of contribution. As an example if the $600 was in lieu of contribution that would mean, in reality, the two other members would be contributing$300 each towards the account. Meaning it results in the service being more expensive for those two members. Initially $250. Not mathematically logical? 6. ## Re: tried to use problem solving process for my problem OK, got it. What ought to happen is he bills the corp$600, and the cost of that $600 is split three ways ($200 each owed by the 3 partners). The net of this is that the two members pay the one who does the mowing a total of $400. In essence he pays himself the other$200.

Maybe this explanation would help: Call the partner who does the mowing 'A' and the other two 'B' and 'C. If A was to provide this service to some outside customer of his and charged $600 he would make a profit equal to his fee minus expense: P_A = Profit for partner A =$600 - Expense

In this scenario partners B & C are not involved, so their "profit" is $0, and P_B=P_C=0. Now suppose A provides this service to the partnership. Consider two cases: Case 1. Partners B and C both pay$300 each. In this scenario the result is: P_A = 600-expense, P_B = -300, P_C = -300. The loss in profit for having the lawn mowed is greater for B and C than it is for A, and hence B and C carry a larger burden. Unfair.

Case 2. Partners A, B and C each pay $200 for the service. Result is: P_A = 600 - expense - 200, P_B= -200, P_C = -200. The change in profit for each partner is the same, so the burden is equally shared - a fair approach. All this assumes that the$600 fee is reasonable and market-driven (i.e., it's the same fee he would charge a different client with similar size of lawn, terrain, etc).

7. ## Re: tried to use problem solving process for my problem

Thank you ebaines

The last assumption, the fee being reasonable and market driven had been justified.

Comparative cases, case 1 and case 2 and substitutuing partners for A B & C makes it easier to slot into the problem solving process.

Thanks again.