In many questions like the one below, algebra simplifies things… but the tricks of the fire certificate can also create nice surprises. Here is a case where they offer a nice simplification without x, there Where z.
Fifteen couples live in a village. Each has one, three or five children, but there are as many couples with one child as there are couples with five. How many children are there in this village?
Answer
If each couple with five children lends two to a couple with one child, we get 15 couples with three children, so 45 children in all.
Of course, we can transpose the idea into algebra by noting x, there and z the number of couples having respectively 1, 3 and 5 children.
The data provides both equations x + there + z = 15 and x = z which gives 2 x + there = 15. The number of children is N = x + 3 there +5 z = 6 x + 3 there = 3 (2 x + there) = 45.
A dead end would be to want to calculate the values of the three unknowns because the solution is then not unique.
Learn more about Hervé Lehning
Normalien and agrégation in mathematics, Hervé Lehning taught his discipline for a good forty years. Crazy about cryptography, member of the Association of encryption and information security reservists, he has in particular pierced the secrets of Henri II’s cipher box.
Also to discover: The universe of secret codes from Antiquity to the Internet published in 2012 by Ixelles.
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