The initial problem was stated wrong Andrew the eldest son was to get 1/2 of the horses...2nd son 1/3 of the horses and youngest son 1/9 (not 1/6 as originally stated) of the horses. Add the fractions and you find they were left only 17/18th of the horses. Working the arithmetic from there you will see that each of the sons got more horses than he was entitled to because when the 18th horse was added all of the "fractional horses" created when dividing 17 rounded up. But since the sons were only left 17/18th of the horses there was still one left over which the cowboy rode off into the sunset.
Who said Mathematics is a perfect science.
- Thread starter Bob Wemm
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Russianwolf
Member
This reminds me of the old fun maths problem we did at school.
How many can remember this one?
Three people eat in a restaurant when finished, the waiter brings the bill for $30.
Each person puts in $10.
The waiter takes the money to the cashier who finds that the bill should have only been $25, so gives the waiter $5 change.
Now the waiter isn't good at maths and can't figure out how to split $5 between three so puts $2 in his pocket and gives each of them $1 each.
So, each person paid $10 and got back $1, so $9 each right?
3 x 9 = 27 plus the $2 in waiter's pocket
27 + 2 = 29
Where is the last missing dollar?????
Actually is 3x9 = 27 + the $3 in THEIR pockets is $30. The Waiter's $2 is in the $27.
There is no missing dollar...The diners spent $27.00. $25 for lunch and $2 for the unauthorized TIP. Remind me not to go to lunch with anyone who was confused by this problem.:biggrin::biggrin::tongue:
Russianwolf
Member
1/2 = 9/18 *17 = 8.5
1/3 = 6/18 *17 = 5.66
1/9 = 2/18 *17 = 1.88
1/18 = 1/18 *17 = .999
18/18 = 1 *17 = 17
except that the State is now going to want the horse that was not willed to anyone, and as you can see 1/18th of 17 horses is closer to a whole horse than the fractions of the others. :wink:
l I know is
1 2 3 4 5 ....... 10 9 8 7 6....... 5+6 yep, I still I eleven fingers.
Why convert to decimal? Just work it with fractions.
Rangertrek
Member
Magic Box
OK, check this one out.
Azulejos - YouTube
Similar to some of the above solutions. I like the chocolate better!
OK, check this one out.
Azulejos - YouTube
Similar to some of the above solutions. I like the chocolate better!
Are you sure it was stated wrong? The idea is likely that the last person gets the shaft, while the other two get extra....
My rationale for this is that 1/2 plus 1/3 plus 1/6 is exactly one...
Trust me Andrew it is 1/9th - I first encountered this problem in elementary school roughly 65 years ago, and have seen it dozens of times since - the object was to show that nobody gets screwed and the "wise old man", "wandering cowboy", "small town lawyer" or whoever you want to come along gets to keep his own horse. We were given this as a fractional arithmetic problem - the student was to figure out that the dead person only left his sons 17/18ths of his horses......
A man driving a flock of sheep met another person who asked "How many sheep are in that flock?" the shepherd said "Well if I had as many more and half as many more and two and a half, I would have a hundred". How many sheep did he have. If you want to make it interesting do it forgetting that you know anything about algebra .... strictly arithmetic. I got this as a sixth or 7th grade arithmetic problem.
Bob Wemm
Member
Only 39.
And I like the 10 9 8 7 6 and five on this hand, makes 11 fingers. Got 11 toes as well.
Bob.
And I like the 10 9 8 7 6 and five on this hand, makes 11 fingers. Got 11 toes as well.
Bob.
Waluy
Member
I am coming up with 20. But then again I can't do it with out using algebra, I have always solved using variables even before they taught me what they were.
In arithmetic.
Using only arithmetic it is what he has now + what he has now + 1/2 what he has now + 2 1/2 = 100
so adding 2 1/2 what he has now +2 1/2 = 100
so 2 1/2 what he has now = 100 - 2 1/2 = 97 1/2
so what he has now = 97 1/2 / 2 1/2 = 195/2 / 5/2 = 195/2*2/5 = 390/10 = 39
using rules or elementary arithmetic.
Algebra is simple x=number of sheep
x+x+.5x + 2.5 = 100
2.5 x = 100-2.5
2.5x = 97.5
x= 97.5/2.5 = 39
Bob Wemm
Member
HOORAY, i got it right.
Bob.
Bob.
Russianwolf
Member
actually you are doing algebra both times, you are just using fractions to solve one and decimals to solve the other. Anytime you have a number that you don't know and are solving for, its algebra. you can us a letter or words to define it, but its still the same.
As far as solving it fractionally you could have also done it this way
x = 97 1/2 / 2 1/2 = 195/2 / 5/2 = 195 / 5 = 39
Waluy
Member
Ah I see where I made my mistake for some reason I was reading the last part as an extra two and a half times what he had, not that he had an extra two and a half sheep. So I was coming up with:
x+x+.5x+2.5x=100
5x=100
x=100/5 = 20
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My teacher would have scolded you for not showing inverting 5/2 and stating that the two's cancel leaving 195/1*1/5=195/5. We were not allowed to do that in our heads for written problems.
Actually you are not using the rules of algebra to solve it fractionally you are using the rules of arithmetic and can solve the problem without ever stating it as an algebraic equation and with no knowledge at all of algebra per se. My dad never saw an algebra text while in school and could solve many of the problems I got in beginning algebra.
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