# An ingenious mix

They say that an honest and simple milkman who boasted of his correction and the fact of never having disappointed a client discovered with distaste one morning that his milk supply was insufficient to meet the demand of all his clients. Indeed, their reserves were insufficient to supply all customers with their usual route and they had no chance of getting more milk.

Noticing the lousy effect that this could have on your business, not to mention the disappointment and discomfort it would produce for your customers, I kept thinking of a solution.

After many laps he decided that he could not attend to some clients and ignore others so he would have to divide what he had among all so that he made the decision to dilute the milk with enough water to supply all the demands . When he found, after a diligent search, some extremely pure water that he could use for his purpose, he put in one of the vessels the amount of gallons of water that would allow him to serve all his clients.

However, as he used to sell milk of two qualities, one for eight cents a quarter, and the other for ten, he set out to produce two mixtures in the following ingenious way:

From vessel number 1, which only contained water, it poured enough to double the contents of vessel number 2 that contained only milk. Then, he poured from number 2 to number 1 an amount of the mixture equal to the amount of water he had left in number 1. Then, to ensure the desired proportions, he proceeded to pour from number 1 the amount sufficient to double the content of the number 2. This left the same amount of gallons in each vessel, as can be demonstrated, although in vessel number 2 there were two gallons more water than milk.

The process is not as complicated as it seems since only three changes are necessary to match the contents of both vessels.

Can you determine exactly how much water and how much milk each vessel finally contained?

#### Solution

The honest milkman began with 5 gallons of milk in the Number 2 vessel and 11 gallons of water in the Number 1 vessel.

The operations described will result in 6 gallons of water and 2 of milk in the first vessel and 5 gallons of water and 3 of milk in the second.