How much were the coins worth?

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Drews

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How much were 43 coins worth? Given a note from the mint did say that the shipping charge would be based on the total weight of the coins, 304.588 grams. All pennies, nickels, dimes, quarters, half-dollars, and dollars enclosed had been freshly minted and stamped 2012.
 
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Are these United States coins? Did you go to the US Mint's web site, to look up the weight of each coin type in grams? Do you know how to set-up and solve a system of equations? What class are you in, and what are they doing?

In future requests for help, please follow the main points in our posting guidelines.

Cheers :cool:
 
We cross-posted.

Why are you now talking about a shipping charge?

Please read the page referenced in my first reply. Then come back and add a new post containing #1 and #3.
 
I'm trying to make it short, but anyway here's the whole thing:


It was a hot and humid Tuesday, and all was calm in Mayberry. Suddenly, in a lather, Floyd the
barber bursts into the sheriff’s office, crying “Thief! Thief!”
Deputy Barney, obviously just awakened by the shouting, stumbles out of the back room, pistol
drawn, fumbling for the .38 cartridge in his pocket. “What? Who?” Seeing Floyd there, he reluctantly
holsters his weapon, sits behind the sheriff’s desk, takes out his notebook, and begins the interrogation.
“What? Who?” he repeats, styfling a yawn.
“I don’t know who, but I’ve been robbed,” replies the barber, out of breath. “I left my safe door
open and walked across the street for an ice cream soda. When I returned twenty minutes later, I
discovered that a sack of coins had been taken from the safe. Oh, my, oh, my! I knew I should have
locked it! They didn’t touch the bills, though, so I suspect it was kids, maybe that little red-haired boy.”
“Well, I doubt it was Opie. But how much was taken?”
“Forty-three coins.”
“What? No, I mean how much were the coins worth? Forty-three coins could be worth anything
from 43¢ to $43.00.”
“I don’t know, I was going to put them in my cash register this afternoon. But an accompanying
note from the mint did say that the shipping charge would be based on the total weight of the coins,
304.588 grams. Oh, and the note proudly said all pennies, nickels, dimes, quarters, half-dollars, and
dollars enclosed had been freshly minted and stamped 2012.” “Well, for my police report, I’ve got to know the value of the stolen property, Floyd.”
“Barney, what am I going to do? I need those coins for my register.”


I went to US mint website, did a bunch of different combination, and I got 14 dollars for all the coins. And left with 1.648 grams, by taking 304.588 - 302.94.
 
You're not very good at answering direct questions. The way to "make it short" is to follow our directions. Exactly what kind of help do you expect to receive here?

It seems that you desire to chat about a puzzle; hence, I have moved your thread into the faculty lounge. Chat away. :cool:
 
Hello, Drews!

Where in the world did this problem come from?
It's rather silly. .It has way too little information.

How much were the 43 coins worth?
A note from the mint said the shipping charge would be based on the total weight of the coins, 304.588 grams.
All pennies, nickels, dimes, quarters, half-dollars, and dollars enclosed had been freshly minted and stamped 2012.
Click to expand...

Let \(\displaystyle \begin{Bmatrix}P &=&\text{no. pennies} \\ N &=& \text{no. nickels} \\ D &=& \text{no. dimes} \\ Q &=& \text{no. quarters} \\ H &=& \text{no. half-dollars} \\ S &=& \text{no. silver dollars} \end{Bmatrix}\)


And suppose we know the unit weights of the coins:

. . \(\displaystyle \begin{Bmatrix}w_p &=& \text{weight of a penny} \\ w_n &=& \text{weight of a nickel} \\ w_d &=& \text{weight of a dime} \\ w_q &=& \text{weight of a quarter} \\ w_h &=& \text{weight of a half-dollar} \\ w_s &=& \text{weight of a silver dollar} \end{Bmatrix}\)


We have:
. . \(\displaystyle w_pP + w_nN + w_dD + w_qQ + w_hH + w_sS \:=\:304.558\)

We also know:
. . \(\displaystyle P + N + D + Q + H + S \:=\:43\)

Two equations, six unknowns.


And we're supposed to find the total value of the coins.

. . \(\displaystyle V \:=\:p + 5N + 10D + 25Q + 50H + 100S\)


Good luck!
 
soroban said:
Let \(\displaystyle \begin{Bmatrix}P &=&\text{no. pennies} \\ N &=& \text{no. nickels} \\ D &=& \text{no. dimes} \\ Q &=& \text{no. quarters} \\ H &=& \text{no. half-dollars} \\ S &=& \text{no. silver dollars} \end{Bmatrix}\)
Click to expand...

They could be American Silver Eagle $1 coins (I bought three 2012 proofs in two versions).

Or, they could be 2012 presidential dollar coins.

Or, they could be 2012 Sacajawea dollar coins.

With the latter two, there are multiple versions (circulating, silver, proof, special) -- each has its own weight.


The half-dollars are just as problematic.


The remaining coins could all be considered circulating versions (i.e., coins minted for commerce), or maybe not. There are various proof versions of all of them.


The puzzle is not well-designed.
 
He is not exactly the Math-type teacher, so this is the best he can come up with. Beside this silly little puzzle is for my programming class. So as long as I have the equations that soroban gave, I'm just gonna let computer do all the hard stuff.
 
Drews said:
this silly little puzzle is for my programming class
Click to expand...

It took 90 minutes for you to post it, but you finally provided some useful information, lol.

What programming language are you using?
 
Nice, Denis. (You looked up some weights, I presume.) I happen to know that 11.34g is correct for the Kennedy half-dollar coin that is available in rolls or certain annual sets. Don't know nuthin' about any of the rest (except American Eagle proof dollars).
 
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Oh, I just noticed that the original post (edited) implies some 2012 quarters were enclosed in the 304.588g package.

Maybe that is another goof from machine teacher. ;)

Our 50-cent coins are a tad larger in diameter and thicker than our circulating dollar coins. Those dollar coins contain four or five elements; the 50-cent coins contain only one or two (could be the denser elements, I dunno).
 
mmm4444bot said:
What programming language are you using?
Click to expand...
I'm using VB right now, and learning about some OOP.

And thanks Denis for provided me the solution, that way I can confirm if my codes were alright.

Now I just have to scratch my head on how to write it.
 
I'm thinking that Denis used nested loops to generate all possible sets of coins (from 43 pennies to 43 dollars, and every possible combination in between) while comparing the combined weight of each set with the known total, using the specific per-coin weights posted. A common list of print commands was likely coded for each match.

He discovered that only one combination matched.
 
Thank you so much for the information. That's gonna help me a lot when I write code. I need every help and resource I can find for this project.

Well, he did say I can use any resource for helps, except him. I have one more question, is it easier to write it in pseudo-code or an actual program?
 
Pseudo code is much easier, where accepted. If you are required to submit a working program for this assignment, then you'll eventually need to write one.

Judging the easiest approach to completing a working program is a subjective decision. Some programmers like to play around with some quick flowchart sketches or algorithms on scratch paper and then dive right into coding -- working out details through ongoing testing, debugging, and revising (me). Other programmers are more disciplined, and they find it easier to write-out the entire program algorithm in a way that allows them to then code the whole program at once (not me).

With a lot of nested loops involved, I would definitely sketch something first, using a list of main variable names chosen ahead of time; parts of that scratch paper would look like pseudo code.

It's really a personal decision. If you find that you're spending a lot of time at the keyboard reworking code because of logic errors, then you should spend more time planning.

Otherwise, do it your way and have fun. :cool:
 
Denis said:
A few pointers:
p=pennies, n=nickels, d = dimes, q=quarters, h=halfbucks, b=bucks

multiply each weight by 1000, so your target is 304588 (much easier than using decimals):
2500p + 5000n + 2268d + 5670q + 11340h + 8100b = 304588

The coefficients can be made smaller by dividing each side by 2:

1250p + 2500n + 1134d + 2835q + 5670h + 4050b = 152294
Click to expand...

...
 
Thank you all so much. All of your helps and suggestions gonna make my life a lot easier when I write the code. Sorry I can't reply immediately, it's almost the end of semester now, so the teacher push a lot of projects. Just write what you have in mind and I will see it later.

Appreciate for all the help so much!
 
Can you guys help me a little more with the programming stuff, I'm lost here.
 
Drews said:
Can you guys help me a little more with the programming stuff, I'm lost here.
Click to expand...

Show us your work and strategy - we can help after that.

Denis had written a code for you - and posted - use that as a starting point.

You have not shown a single line of work in all your previous posts.
 
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