You didn’t lose $100. $3000 came in, $2300 went out. $700 profit. That is all that matters. The difference between Sale 1 and Purchase 2 isn’t relevant. What matters is the AMOUNT of Purchase 2, not the coincidence that it is close to Sale 1.
This would be instantly obvious if you restated the problem this way:
“I bought two reindeer for $900 and $1400 and sold then for $1700 and $1300. In total, what was my profit?”
That way the closeness of the numbers 1300 and 1400 doesn’t seem relevant. Or reverse the order - say you bought for $1400 and sold for $1700, THEN bought for $900 and sold for $1300. It would never occur to anyone if it was phrased that way that you “lost $100.”
Sure you did. Suppose you always had the reindeer, and never sold it at the end. The only transaction was temporarily selling it for $1300 and buying it for $1400. You lost $100 there.
The profit here is -A + B - C + D. You can group this as (D - A) - (C - B), like I did above. That’s the beginning-to-end profit minus the loss in the middle. You can group it as (B - A) + (D - C), which is the profit in the first buy-sell operation plus the profit in the second. You can ignore any grouping and just add sales and subtract costs.
What you can’t do is group it as (B - A) - (C - B) + (D - C), since that overcounts the losses.
I don’t think the closeness of the numbers has anything to do with it. I think it’s that you sold an item for $1300, and so you think “it’s worth $1300”. So, when you buy that same item back for $1400, you think you overpaid by $100. It would work even if you bought it back for $20000.
To me, the best way to get around that issue is to just look at money in vs. money out. Ignore the reindeer altogether, and treat it like you’re balancing a checkbook. You start with no reindeer, and you end with no reindeer, so the reindeer doesn’t matter.
You can also put the middle transaction in a different currency. You buy a reindeer for $900. You then sell it for 13 magic beans. You buy it again for 14 magic beans, and then sell it for $1700. What’s your profit?
Well, you made $800, but you’re out one magic bean. If a magic bean is worth $100, it’s the original problem again, and you really only made $700 profit.
This looks like the most authoritative source I’ve found yet and they just call it a “complex word problem”.
We consider complex word problems to be mathematical word problems that typically (1) present information in a syntax that does not merely mirror the mathematical task, (2) contain information that might be redundant or superficial, (3) contain multiple representations, and (4) revolve around a context that is functional for the problem solution
Which is pretty disappointing when what you are looking for is a single memorable word. Myself, I propose “puzzlequandrum”, as invented just now by ChatGPT.
Sure, but the point is that it’s reasonable to look at those middle two transactions as a loss. Those were the only ones involving magic beans, and so that’s how you ended up with a one-bean loss.
When the currencies are the same, there are other ways of interpreting the gains/losses. They are all perfectly equivalent as long as you’re careful.
Sure, you can put transactions 2 and 3 into a different currency. You could also put 3 and 4 in a different currency, in which case you can’t combine the middle two transactions.
Hence post #22, where I said there were multiple valid groupings.
What I am arguing against is RickJay’s claim that (C-B) is “not a relevant number at all”. It absolutely is, from one (valid) way of looking at the problem. It’s not coincidental, either.
There are many math problems which are complex or involve some narrative details. The question in play is an attempt to be tricky, hence the decoy. Catching a train of specific speed to Chattanooga or figuring out the weight on a pulley don’t usually involve anything missing.
If you lift a 100kg stone by means of a pulley which is suspended on a tree’s branch by pulling with 101kg of downforce on the rope … does the branch see:
My favorite example of this sort of problem, best said aloud:
You’re driving a bus, and there are 32 passengers. At the first stop, 5 passengers get on, and 3 passengers get off. At the second stop, 7 passengers get on, and 15 passengers get off. At the third stop, 20 passengers get on, and none get off. At the four stop, all but four passengers get off, and three passengers get on. How old is the bus driver?
At the risk of beating a dead reindeer, I think I see the root of the disagreement. It comes down to how one values the reindeer during this process. To illustrate how one can bookkeep a $100 loss or not for the same set of transactions, let me tell you about my company.
Luminaria, LLC (I paid a bunch of consultants a lot of money to come up with this name. Hell if I know what it means.) is in the business of buying and selling reindeer. For FY 23, we had the following quarterly activities.
Started the year with 0 reindeer and $10,000 in cash;
Q1: (bought a reindeer for $900) Inventory: 1 reindeer, Cash: $9,100
Q2: (sold a reindeer for $1300) Inventory:0 reindeer, Cash: $10,400
Q3: (bought a reindeer for $1400) Inventory: 1 Reindeer, Cash: $9,000
Q4: (sold a reindeer for $1700) Inventory: 0 reindeer, Cash: $10,700)
A slow year, but I did make $700 on sales of $3,000 (23% Margin, not bad). Did I lose substantial money quarter to quarter? No, because I have reindeer, which add to my Total Assets.
Anyway, the bookkeeping issue is in how we determine our total assets at any given time, which depends on the value of Cash (simple to determine) plus the value of inventory (harder). I’m going to choose to value reindeer in inventory in two ways. (1) Value= price paid; and (2) Value = $1300 (I could imagine a value established by some mythical market price at any given time, but that way lies madness). So, tracking Total Assets at the end of each quarter over the year using method (1) and method (2):
Note the difference. (1) shows no losses during the year in total assets. (2) shows a $100 loss between Q2 and Q3 (and yes, I deliberately chose $1300 as the fixed value). Counting this loss is entirely dependent on your method of valuing reindeer. (BTW, picking a bigger or smaller fixed cost asset valuation will simply show bigger swings during the year, but end up at the same point as far as total gain)
Imagine you had a balanced situation with two 100kg weights suspended from the branch with a pulley in the middle. That would clearly require the branch to support 200 kg of weight. Now you add an another kg to one side of the balance. This describes your situation.
