Three women are dying to get the Prada bag from the latest fashion show, but neither could afford to pay the $1,200 that the bag is offered for. First woman is saying: "If each of you two will give me half of what you have, I will have enough to buy the bag. We could then share bag proportionally to our investments." Second is saying: "If each of you will give me one third of what you have, I will also have enough to buy this bag." Then the third woman that stayed quiet all the time, said: "If each of you two will give me just one fourth of what you have, I could buy this bag." How rich each of these women is?
(believe it or not, but this puzzle is 500 years old!)
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4 comments:
first friend has: $352.94122
Second friend has: $776.4707
Third friend has: $917.64716
Alin, this looks like voodoo.
Could you explain, please, so we all will get it.
I came up with a set of 3 linear equations with 3 unknowns and used an online matrix calculator to solve it.
this is the set of equations:
a + 1/2b + 1/2c=1200
1/3a + b + 1/3c=1200
1/4a +1/4b + c =1200
it can be represented in matrix form:
1, 1/2, 1/2 a 1200
1/3, 1, 1/3 b 1200
1/4, 1/4, 1 c 1200
----------- - ----
A X B
To solve X = A-ˡ * B
(A-ˡ is the inverse matrix of A)
I googled the terms "solve equation with matrix"
and "matrix calculator"
This document has a very good explanation on Using the inverse matrix to solve equations:
http://www.mathcentre.ac.uk/resources/leaflets/firstaidkits/5_6.pdf
I used an online matrix calculator and came up with the results.
Puzzle a day will keep Alzheimer away.
This one definitely will.
Bravo, master Alin!
I know this was hard for many.
But linear equations with three unknowns could also be solved with pre-historical tools of pen and paper.
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