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Posted: 1/8/2005 10:51:13 PM EDT
[Last Edit: 1/9/2005 1:18:28 AM EDT by All_Beef_Patty]
You are a veterinarian. You have purchased a large balance scale on e-bay, but no weights were included. You want to use the balance scale to weigh animals. Assume the weight (in pounds) of every animal is an integer value less than 100.

A friend tells you that Balance Scale Weights R Us is a good place to purchase weights for balance scales. You visit BSWRU and talk to Rico, the mathematician turned weight salesman. Sensing that you're up to a unique challenge, he offers you two deals:

1. He has a standard weight set containing the following weights: 1, 1, 1, 1, 5, 10, 20, 20, and 50 pounds. He will sell this to you for $X.

2. Alternatively, he will custom-make a set of magical math weights.

Here's how the math weights work:
Rico will sell you a combination of numbers and mathematical symbols. Then, he will combine them however you like and magically turn them into weights equal to the numerical answer. For example, if you buy a "7", a "2", and a "^" Rico could use them to create a 128-pound (2^7) or 49-pound (7^2) weight. However, once a weight is created, you are stuck with it. You can't uncombine or add to the formula.

Rico has plenty of symbols, but he is in short supply of numbers. In fact, he only has 9s. Here are the prices for his numbers and symbols:

Each "9" costs $1.00.
Each simple arithmetic expression (+,-,*,/) costs $0.25.
His other arithmetic expressions (!,sqrt,^) cost $0.50 each.
Parentheses are free.

You're not exactly a penny-pincher, but you're intrigued by Rico's challenge. You want to have enough weights to be able to be able to calculate the exact weight of any animal less than 100 pounds. (Remember they all have integer weight values.)

What value of X makes the two alternatives equal?
Link Posted: 1/8/2005 10:55:25 PM EDT
Someone should beat you with a textbook.
Link Posted: 1/8/2005 10:58:23 PM EDT
Been eating beef? Can you say "Mad Cow"
Link Posted: 1/8/2005 11:01:13 PM EDT
D. All of the above
Link Posted: 1/8/2005 11:02:34 PM EDT





That's why I dropped out of  math, they started mixing in the alphabet!!
Link Posted: 1/8/2005 11:04:15 PM EDT




Crap. I tried...I f-ing tried to get this..God damn
Link Posted: 1/8/2005 11:06:04 PM EDT
Link Posted: 1/8/2005 11:09:44 PM EDT
0
Link Posted: 1/8/2005 11:33:24 PM EDT
It's late.

X=$43.00
Link Posted: 1/8/2005 11:44:21 PM EDT

Originally Posted By Zack3g:
Someone should beat you with a textbook.



LOL.

There's a reason I failed Algerbra 2.
Link Posted: 1/9/2005 12:03:20 AM EDT
[Last Edit: 1/9/2005 12:14:37 AM EDT by HIPPO]
Just fooing around I came up w/ x = $32.50 $27.25
Link Posted: 1/9/2005 12:03:40 AM EDT

Originally Posted By GabbasaurusRex:

Originally Posted By Zack3g:
Someone should beat you with a textbook.



LOL.

There's a reason I failed Algerbra 2.



Algebra  

I hate math. My worst subject.
Link Posted: 1/9/2005 12:09:33 AM EDT

Originally Posted By HIPPO:
Just fooing around I came up w/ x = $32.50



Nice try.... but no, it can be done with less than $32.50!

Any other guesses?
Link Posted: 1/9/2005 12:15:43 AM EDT
Ya know what I think...

I think someone surfed ARFCOM a little too long and did not get his math homework done, so he posts it here hoping that some one will solve it...because why would any one, normal, person want to post teasers like that for fun?

Don't worry...I've done it too.  
Link Posted: 1/9/2005 12:15:46 AM EDT

Originally Posted By All_Beef_Patty:

Originally Posted By HIPPO:
Just fooing around I came up w/ x = $32.50



Nice try.... but no, it can be done with less than $32.50!

Any other guesses?



See my edited answer.
Link Posted: 1/9/2005 12:24:32 AM EDT
I'm at x=33.  I must be missing something.

Steve
Link Posted: 1/9/2005 12:32:26 AM EDT

Originally Posted By Steve_:
I'm at x=33.  I must be missing something.

Steve



Hint: you don't actually need, 1, 1, 1, 1, 5, 10, 20, 20, and 50.
Link Posted: 1/9/2005 12:39:31 AM EDT
[Last Edit: 1/9/2005 12:43:57 AM EDT by Steve_]
I'm down to x=16

Steve

ETA:

          Value    Quantity   Price  Total

9/9         1              2         2.25  4.50
sqrt(9)   3              2         1.50  3.00
9            9              2          1.00  2.00
9+9       18            2          2.50  5.00
9!          45            1          1.50  1.50
                                                  16.00
Link Posted: 1/9/2005 12:41:57 AM EDT
[Last Edit: 1/9/2005 12:43:56 AM EDT by SilentStalker]

Originally Posted By All_Beef_Patty:
Hint: you don't actually need, 1, 1, 1, 1, 5, 10, 20, 20, and 50.


edited do to this info
Link Posted: 1/9/2005 12:44:07 AM EDT
Link Posted: 1/9/2005 12:45:22 AM EDT
[Last Edit: 1/9/2005 12:48:40 AM EDT by HIPPO]
Alright, I am down to $16.25 $14.25!

back to the abbacus!

shit
Link Posted: 1/9/2005 12:45:58 AM EDT
[Last Edit: 1/9/2005 12:48:13 AM EDT by ColonelKlink]
Link Posted: 1/9/2005 12:47:17 AM EDT
doh!  right, that's 9*8*7...

Dumass me

Steve
Link Posted: 1/9/2005 12:51:30 AM EDT
Now i'm back up to x=18.50.


Steve
Link Posted: 1/9/2005 12:51:55 AM EDT
Link Posted: 1/9/2005 12:58:43 AM EDT
Alright, I am at $17. 50 or $18.50 depending on the answer to a question I have.
Link Posted: 1/9/2005 1:04:10 AM EDT
Link Posted: 1/9/2005 1:04:21 AM EDT
Isn't 42 the answer to life, the universe and everything?
Link Posted: 1/9/2005 1:09:42 AM EDT
[Last Edit: 1/9/2005 1:13:50 AM EDT by ColonelKlink]
Link Posted: 1/9/2005 1:18:12 AM EDT
SOLUTION


We need only buy the integer powers of 3, from which we can add and subtract to form other numbers, by putting weight on the same or opposite sides of the scale respectively.
This is also efficient because of their relationship to the number 9.


1=9/9 --> $2.25
3=sqrt(9) --> $1.50
9=9 --> $1.00
27=9xsqrt(9) --> $2.75
81=9x9 --> $2.25
______________________
Total: $9.75
Link Posted: 1/9/2005 1:20:17 AM EDT
[Last Edit: 1/9/2005 1:22:41 AM EDT by ColonelKlink]
Link Posted: 1/9/2005 2:03:06 AM EDT

Originally Posted By All_Beef_Patty:
SOLUTION


We need only buy the integer powers of 3, from which we can add and subtract to form other numbers, by putting weight on the same or opposite sides of the scale respectively.
This is also efficient because of their relationship to the number 9.


1=9/9 --> $2.25
3=sqrt(9) --> $1.50
9=9 --> $1.00
27=9xsqrt(9) --> $2.75
81=9x9 --> $2.25
______________________
Total: $9.75




It's bad enough you give us an math problem at 4:00 am.  You didn't have to go and make it a trick question too!

Steve

Link Posted: 1/9/2005 3:45:06 AM EDT

Originally Posted By Zack3g:
Someone should beat you with a textbook.



+1
Link Posted: 1/9/2005 4:14:03 AM EDT
Gimme that book, when you are done!
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