Question

A recent television commercial advertised the sale of "gold coins" that were actually buffalo nickels clad in 12mg of 100% gold. For the unbelievable low price of only $9.95 you can own one of these treasured pieces of gold normally sold for over $50.00! Calculate the actual value of the coin (i.e. the current value of the gold present, plus the face value of the coin - ignoring any added historical numismatic value that a buffalo nickel may warrant). The market price of gold is given in troy ounces where 1 troy ounce = 31.1g. Have to show work and I have no clue how to do this one.

Answer 1

I have to use Dimensional Analysis to figure out the answer.

Answer 2

It says the gold coin is normally sold for 50 dollars.
What is the weight of a bufallo coin.

Answer 3

It doesn't give me the weight of a buffalo coin.

Answer 4

"Calculate the actual value of the coin (i.e. the current value of the gold present, plus the face value of the coin - ignoring any added historical numismatic value that a buffalo nickel may warrant). "

Answer 5

Focus on this:
"the current value of the gold present, plus the face value of the coin"

Answer 6

What is the face value of a nickel?

Answer 7

So I need to look up the current value of gold? And a nickel is worth 5 cents.

Answer 8

Correc t.
Start with 12 mg.
Find the values of 1 troy ounce of gold.
Then use the conversion of 1 troy ounce = 31.1 g

Answer 9

Amg I understand it now, thank you so much! I was so confused by all the extra wording and numbers in the problem. Thank you for breaking it down like that. I know how to set it up now. Ty so much<3

Answer 10

Great.
When you finish, let me now what you get.

Answer 11

Okay, working it out now.

Answer 12

I'm still working it out. Having a little trouble with the setup. But I think I almost have it.

Answer 13

Great. Take your time. Do it carefully and don't rush.

Answer 14

Ugh I think I'm confusing myself trying to set it up in dimensional analysis form. I'm trying to convert from mg -> grams -> troy ounces. I have 12mg of gold. 1g = 1000mg. So 12mg of gold is equal to .012g of gold. There's 31.1g in 1 troy ounce. And then I get confused. >_<

Answer 15

I need to convert .012g to troy ounces, but I'm not sure how to do that. I think I'm making this much harder than its suppose to be.

Answer 16

\(12 ~mg \times \dfrac{1~g}{1000~mg} \times \dfrac{1~oz}{31.1~g} \)

Answer 17

In dimensional analysis, every conversion factor is a fraction.
You write the fraction in a way that the units you don't want cancel out, and the units you want stay.

Answer 18

I had the first part set up correctly but I was doing the third part with troy oz and g backwards. So I'm dividing .012g by 31.1g? I'm getting this ridiculously large number though. 3.86 x 10^4

Answer 19

You don't need to calculate it yet.
You can calculate it at the end when all conversion factors are done.
You still need the cost of gold.
Did you find how much an ounce of gold is worth today?

Answer 20

Oops I forgot that that was part of the conversion also. It says that 1g of gold is worth $36.08.

Answer 21

That is fine, but the problem specifically states that the price of gold is given in troy ounces, and it even has the conversion from troy ounces to grams.
Do you find the price of gold in troy ounces?

Answer 22

Oh sorry >_<

Answer 23

1 troy ounce of gold is worth $1,122.08

Answer 24

Great.
Let's continue the conversion, now including 1 oz = $1122.08

Answer 25

mg cancels mg
g cancels g
We were up to oz in the numerator.
Now we write a conversion factor with $ in the numerator and oz in the denominator, so we cancel oz and keep $.

\(12 ~mg \times \dfrac{1~g}{1000~mg} \times \dfrac{1~oz}{31.1~g}\times \dfrac{$1122.08}{1~oz}\)

Answer 26

I understand where we got all of those numbers and units and why its setup like that. But now I don't think I'm doing the math correctly. I'm still ending up with a large number. You divide 12 by 1000 and that cancels out the grams like you said. You end up with .012g. Then you divide .012g by 31.1g to cancel out the grams correct? Then you are just left with troy ounces. So you divide by $1122.08?

Answer 27

Since you are multiplying fractions, multiply all numerators together.
Then multiply all denominators together.
Then divide the product of the umerators by the product of the demominators.

Answer 28

43 cents + 5 cents for the nickel value, so the actual value of the coin is 48 cents?!

Answer 29

\(12 ~mg \times \dfrac{1~g}{1000~mg} \times \dfrac{1~oz}{31.1~g}\times \dfrac{$1122.08}{1~oz}=\)

\(= \dfrac{12 \times 1 \times 1 \times 1122.08}{1 \times 1000 \times 31.1 \times 1}~ ~$\)

\(=$0.43\)

Answer 30

You are correct.

Answer 31

This is how I did it. When I looked up the price of gold, I got $1116.15 per ounce
The answers are close.

\(12 ~\color{red}{\cancel{mg}}~\color{blue}{\cancel{Au}} \times \dfrac{1~\color{green}{\cancel{g}}}{1000~\color{red}{\cancel{mg}}} \times \dfrac{$1116.15}{1~\color{orange}{\cancel{oz}}~\color{blue}{\cancel{Au}}} \times \dfrac{1~\color{orange}{\cancel{oz}}}{31.1~\color{green}{\cancel{g}}} = $0.43 \)

Answer 32

Omg I feel so stupid! I was trying to do the dimensional analysis by dividing by 1000 then 31.1, and then I had no clue what to do with 1122.08 and I was confusing myself so badly. All I had to do was multiply out the denominators and numerators. I've been making this so hard on myself. Thank you so much mathstudent55. You literally did more than help me solve that question, you helped me fix the entire issue I've been having with dimensional analysis.

Answer 33

There is a quicker way to do this.
Multiply all numerators together, then divide by each of the denominators.
It will give you the same result without having to record a number and use it later.

Answer 34

Start with 12.
As you go right, multiply by each numerator and divide by each denominator.

Answer 35

I'm going to go back and check all the other problems using that method. I can't believe how complicated I was making that.

Answer 36

You are very welcome.
Don't feel stupid. I think you are smart.
You are asking questions about the things you don't understand, so you'll learn them.
In my book, that's smart.

Answer 37

You have no idea how much that means to me. You are the best! Thank you again. I can go to class tomorrow and not be nervous because I actually understand where I've been going wrong. Thank you. <3

Answer 38

You're welcome.
If you have any questions, don't hesitate to ask.
That's how you learn.