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?

Someone should beat you with a textbook.

Been eating beef? Can you say "Mad Cow"

D. All of the above

That's why I dropped out of  math, they started mixing in the alphabet!!

Crap. I tried...I f-ing tried to get this..God damn

0

It's late.

X=$43.00

Quoted: Someone should beat you with a textbook.

LOL.

There's a reason I failed Algerbra 2.

Just fooing around I came up w/ x = $32.50 $27.25

Quoted: Quoted: Someone should beat you with a textbook. LOL. There's a reason I failed Algerbra 2.

Algebra  

I hate math. My worst subject.

Quoted: 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?

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.  

Quoted: Quoted: 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.

I'm at x=33.  I must be missing something.

Steve

Quoted: 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.

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

Quoted: Hint: you don't actually need, 1, 1, 1, 1, 5, 10, 20, 20, and 50.

edited do to this info

Alright, I am down to $16.25 $14.25!

back to the abbacus!

shit

doh!  right, that's 9*8*7...

Dumass me

Steve

Now i'm back up to x=18.50.


Steve

Alright, I am at $17. 50 or $18.50 depending on the answer to a question I have.

Isn't 42 the answer to life, the universe and everything?

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

Quoted: 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

Quoted: Someone should beat you with a textbook.

+1

Gimme that book, when you are done!