Reply
Tue 15 Jun, 2004 08:58 pm
Need help on this one...
My ranch, said the Texan I met in class, is a rectangle, and very nearly a square. The length is one-fifth of a mile more than a whole number of miles, and the width is one-eight of a mile more than the same whole number of miles.
And, oh yes, the area is a whole number of square miles. Now then, can you tell me the area of my ranch?
Well, I think so. But first, tell me, is your ranch bigger than the state of Rhode Island?
Gosh, no he replied. Its nothing like that.
Then I know the area of your ranch, I told him.
What is the area of his ranch, and how did I know it?
Please let me know if you can help...
Thanks...
OK, 0.125 x 0.2 = 0.025.
So, 0.2 + 0.125 = 0.325.
Then, (0.325 x 3) + 0.025 = 1
That makes the ranch 3.2 miles x 3.125 miles doesn't it?
Where is the clue in "smaller than RhodeIsland" Adrian?
Dunno Kev, I assume that there are other answers that fit but that they are bigger than Rhode Island. If I was any good at maths I'd work it out but...
Looking at it slightly differently:
Let x be the "whole number" referred to in the first part of the riddle.
Then the legnth of the ranch is (x + .2)
And the width of the ranch is (x + .125)
Therefore the area is (x + .2) * (x + .125)
Which simplifies to x ^ 2 + .325x + .025
Since this area is a whole number, and x ^ 2 is always a whole number, then the other part of the equation (.325x + .025) must also be a whole number.
It is simple modular math to see that x can therefore be any number such that x mod 40 = 3, so x can be 3, 43, 83, etc...
However, since the area is less than that of Rhode Island (which is 1045 square miles) then the only x that would result in a smaller area is the x = 3.
That makes the ranch 3.2 x 3.125 miles. No other x will work given the "smaller than RI" part.
Thank you and welcome pedronunezmd.
As I said, if I were any good at maths... :wink:
Stumble It!
Tweet This
Bookmark on Delicious
Share on Facebook
Share on MySpace