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wojcis

Member

Registered: 2008-12-03

Posts: 1

The Mathematical Milkman of Puzzleland

I was reading through the section of this website on Sam Loyd's puzzles and came across the "The Mathematical Milkman of Puzzleland" and I don't understand how to come up with the solution.  I follow where the table comes from, but I dont understand how to go from the table to x = 7 and y = 3.  Any suggestions?

http://www.mathsisfun.com/puzzles/the-mathematical-milkman-of-puzzleland.html

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: The Mathematical Milkman of Puzzleland

The way I work it out is:

Milk in Can 1 = Milk in Can 2
(1/4)(3x-5y) = (3/4)(3y-x)
Multiply by 4: 3x-5y = 3(3y-x)
Move x to one side and y to other: 6x = 14y
And so: x = (14/6)y

Water in Can 2 = Milk in Can 2 +1
(5/4)(3y-x) = (3/4)(3y-x) +1
Multiply by 4: 5(3y-x) = 3(3y-x) + 4
Simplify: 2(3y-x) = 4
Replace "x" with "(14/6)y": 2(3y-(14/6)y) = 4
Simplify: (4/3)y = 4
Hence: y = 3

Now we know y=3, we also know that x = (14/6)y = 7

Does that make sense?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: The Mathematical Milkman of Puzzleland

That looks fine to me.
There are some typos in the table on the solution page though.

In the 'after doubling Can 1' step, the 'Can 1' cell should have twos on the denominator of each fraction. Also, the milk is missing an (x-y) factor.

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Why did the vector cross the road?
It wanted to be normal.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: The Mathematical Milkman of Puzzleland

Thanks very much, mathsy!

I have redone that page with your corrections, plus my workings from above: The Mathematical Milkman of Puzzleland - Solution

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman