Coffee with milk, please


Tanya Khovanova publishes an irregular but excellent blog about math problems. Of Russian descent, she often uses Russian sources, which are otherwise not very accessible in the Western world. The next problem comes from her blog, and has the Moscow 2011 mathematics olympiad as origin:

1) Coffee with milk, please***
1) Coffee and milk**
In a certain family everyone likes their coffee with milk. At breakfast everyone had a full cup of coffee. Given that Alex consumed a quarter of all consumed milk and one sixth of all coffee, how many people are there in the family?

The above problem would go into the class of problems for which you have n equations and n+1 unknowns. Here’s a classic in this category:

2) A farmer went to the market*
A farmer buys 100 animals for 100 dollars but lost his receipt. Cows are $10 each, pigs are $3 each and chicks are $.50 each. How many of each did he buy?
This puzzle is a ‘classic’, but I don’t know its source. If you do, I’d welcome this information!

When you solved both, you will notice that the solving methods of the two puzzles are totally different.

You can find hints at 126, 116 respectively.

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2 thoughts on “Coffee with milk, please

  1. 2. u didn’t mentioned solution for this problem. Let me solve it from traders point of view.
    if he buys 100 chicks then it will cost him only $50. Now he has bought animals but he has to spend $ 50 more. So, can trade 1 chick and $9.5 for one cow, and 1 chick and $2.5 for 1 pig. This way his count of animals will always remain 100.
    so for remaining $ 50, he can buy max 5 cows for 5 ($9.5 and chick) i.e. 47.5 and 5 chicks. So he has now spent $ 97,5. Now he can easily buy 1 pig for $2.5 and one chick.
    so total count 1 pig, 5 cows and 100 chicks minus 6 chicks i.e. 94 chicks.

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