Road map

Alex Y
This one seems not to be getting much traction. Without solving it, here are the steps I took to get to the solution (only after seeing the general direction that Lewis Carroll took in his solution). Quit reading when you think you have enough of a hint, and find your own solution.

Note: Almost every step I took had alternatives that will get to the same answer, so if my step doesn't seem logical to you, go a different route.

1) Set variables x, y, and z for the number of bottles disposed of (sold or drunk by the salesman) on days 1, 2, and 3. Set v as the cost of each bottle, so selling price is 1.1v and margin is .1v

2) Determine the dollar amount of profit each day in terms of x and v, y and v, and z and v.

3) Since the profit is the same each day, set these equal to each other and eliminate extraneous variables to allow x, y, and z to be expressed in terms of only one variable. (Lewis Carroll chose to express y and z in terms of x, but I chose to express in terms of z because of the next step.)

4) The treasurer tells us the value (at retail) of the z bottles remaining after two days, and that lets us express v in terms of z. So now each fact we know about the wine can be expressed in terms of a single variable.

5) The treasurer says that the profit on all the bottles invested in the business was $0.75 per bottle. We also know the profit each day, and can set the dollar profit in total equal to the sum of the daily profits (or three times any day's profits since we know that they are the same).

6) Solve the resulting quadratic equation, and see that only one of the two solutions is possible with five investors putting in the same number of bottles each.

Like I said, middle school or high school algebra, but MUCH harder than any problem I saw back in the day.

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