## Wednesday, July 15, 2009

### How to afford a Prada bag

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!)

Submit your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Alin Grin said...

first friend has: \$352.94122
Second friend has: \$776.4707
Third friend has: \$917.64716

Maria said...

Alin, this looks like voodoo.
Could you explain, please, so we all will get it.

Alin Grin said...

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.

Maria said...

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.