Loan an Employee
Cam, Chris, and Ragknot are friends who have each started new companies. They talk frequently and decide to share resources when necessary. Since the companies are similiar in nature, the employees are actually able to move from one to another without loss of efficiency.
Cam's business started a little slowly, so he loaned Chris's company and Ragknot's company as many employees as each company already had.
In a few months, as economical conditions changed, Chris's company loaned Cam and Ragnot a number of employees equal to the number each already had.
Cam's and Chris's business really started thriving, in a few months, so Ragknot loaned each of his friends a number of employees equivalent to the number each already had.
After the last loan, each company then had 24 employees.
How many employees did each company originally have?
Cam's business started a little slowly, so he loaned Chris's company and Ragknot's company as many employees as each company already had.
In a few months, as economical conditions changed, Chris's company loaned Cam and Ragnot a number of employees equal to the number each already had.
Cam's and Chris's business really started thriving, in a few months, so Ragknot loaned each of his friends a number of employees equivalent to the number each already had.
After the last loan, each company then had 24 employees.
How many employees did each company originally have?
posted by Zaux at
12:40 PM
22 Comments:
As a side note .. I too have noticed different times and wondered as to the location of posters.
You guys care to share?
My home is in Garner, North Carolina in the USA.
I'm in Watford (just north of London) England. It's 10:57 pm. Hello, world!
Thanks Chris ... 6:21PM here
i'm stuck in Thompson,Manitoba,Canada,eh?
6:52 PM
That's a strange name for a couch!
Cam begins with 39 employees
Chris begins with 21 employees
Ragknott begins with 12 employees
==============
Cam loans 21 to Chris and ragknott gets 12 leaving Cam with just 6 employees a quarter of 24 which he will double twice when he gets the employees loaned back.
Cam now has 6
Chris now has 42
Ragknott now has 24
Now Chris loans out 30 employees doubling both his friends companies. This gives us:
Cam has 12
Chirs has 12
Ragknott has 48
Finally Ragknott splits his company down and leaves all three companies on 24.
Good job Antn'y
OK, let C be Cam's initial staff count, S for Chris and R for Ragknot.
I'll just write the nubers in the sequence C, S, R. After the first exchange:
C-S-R, 2S, 2R
After the second exchange:
2(C-S-R), 2S-(C-S-R)-2R, 4R
which simplifies to
2C-2S-2R, 3S-C-R, 4R
After the third exchange:
4C-4S-4R, 6S-2C-2R, 4R-(2C-2S-2R)-(3S-C-R)
which simplifies to:
4C-4S-4R, 6S-2C-2R, 7R-C-S
All three expressions = 24
4C-4S-4R = 24 => A) C-S-R = 6
6S-2C-2R = 24 => B) 3S-C-R = 12
C) 7R-C-S = 24
A)+B) => 2S-2R = 18 => E) S-R = 9
B)-A) => 4S-2C = 6 => F) 2S-C=3
Substitute for C into C) using F) => 7R +3 -2S -S = 24 => 7R - 3S = 21
Use E) to substitute for S =>
7R -3(9+R) = 21 => 4R -27 = 21 => R = 12.
Subst into E) => S = 21, subst into F) => 39.
So started with (C,S,R) = (39,21,12)
Check: after first swap got (6,42,24).
After second got (12,12,48).
After third got (24,24,24).
So started with Cam 39, Chris 21 and Ragknot 12.
Aaaargh. I was beaten to it. Well done Antn'y.
LOL -good one,Chris,but my couch has made it clear that her name is Pequod.
Hi Knightmare. I like your couch, it's so versatile.
Chris ... you really think Knightmare has a tile couch made by versa. Wouldn't a til couch be quite uncomfortable?
I've never owned any versa furniture.
Darn meds ... heh heh!
mmmm....meant tile couch
Not sure if I mentioned where the couch in-joke started, but see Knightmare's post in "Running order" Sept 30, 2009 for the explanation.
Thanks guys ... I enjoyed that ... my son is a marathoner. In fact last Saturday, he completed his first 32 mile race ... 5 hours 20 minutes runtime ... 10 minute miles for 32 of them ... I bet Knightmasre's couch can't do that.
well thanks Chris-now everyone's going to make couch jokes!
Zaux-right on; ;]
"5 hours 20 minutes"runtime...it gives me a knightmare just to think about spending that much time on my feet.
Sorry Knightmare, but LOL for the last couple of posts and LOL for the couch jokes to come.
And I believe that I've cracked "The Robbery" problem. I'll post that brag on the next available new problem.
Zaux. I'd bet Knightmare's Harley couch could thrash that time.
Harley couch...like i said,88 mph
and Chris...some tells me your not really sorry at all ;{
some=something
Your math looks as crazy as mine.
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