Converstion from cubic centimeters to grams

S

Sweetdaisy186

New member
Joined
Jan 21, 2005
Messages
20
Hey guys!

I am a little confused about this problem. A point in the right direction would be greatly appreciated! Thanks! :)

"A gold and copper bracelet weighs 238 grams. The volume of the bracelet is 15 cubic centimeters. Gold weights 19.3 grams per cubic centimeter, and copper weighs 9 grams per cubic centimeter. How many grams of copper are mixed with the gold?"

Thanks again!
 
What is the density (in grams per cubic centimeter) of the bracelet?

Let "g" stand for the number of cubic centimeters (cc's) of gold you have, and let "c" stand for the number of cc's of copper. You know that g + c must equal 15. Use this fact to create your first equation.

What is the weight, in grams, of one cc of gold? Of two cc's? Of three cc's? Of "g" cc's? Write down an expression for the weight of "g" cc's.

What is the weight, in grams, of one cc of copper? Of two cc's? Of three cc's? Of "c" cc's? Write down an expression for the weight of "c" cc's.

Use these two expressions to create an equation for the total weight of the bracelet.

You now have two equations in two variables. Solve the system for the number of cc's. Back-solve for the number of grams.

If you get stuck, please reply showing how far you have gotten in following the step-by-step instructions above. Thank you.

Eliz.
 
g + c = 15

g=19.3 cc
c=9 cc

I understand how to solve for an equation with two variables. Could I please have a hint about how to find the weight in grams of one cc of copper and gold? Is this a converstion factor? Since one is a volume and one is a mass, is this possible? What do you mean when you say to "back solve for the number of grams?"

Thanks sooo much!
 
They give you how many grams are in a cc. The total weight is 238 g.

So you have:

\(\displaystyle x+y=238\)

\(\displaystyle \frac{x}{19.3}+\frac{y}{9}=15\)

Solve the system.
 
Here is what I have so far....

x=238-y, therefore,(238-y/19.3)-(y/9)=15

Then, to get rid of the decimal, I multiplied everything by 10, and now I am stuck because I can't find a common denominator to get rid of my fractions. Thanks! :D
 
Try this, though they're are different methods.

cross multiply:

\(\displaystyle \frac{9(238-y)+19.3y}{173.7}=15\)

\(\displaystyle 9(238-y)+19.3y=2605.5\)

Can you finish now?.
 
I find x=193 and y=45 to be the solution of the given system. Unfortunately, there is no clear definition of x and y, so I cannot opine on the correctness of the one piece you have reported.

We had nice definitions from stapel for g and c. Why did we lose those?
 
Yes, sweetdaisy, that's what I got. Since x is the grams of gold and y the grams of copper, 193/19.3=10cc of gold and 45/9=5cc of copper. 10+5=15cc in the bracelet. 193+45=238g bracelet. Seems OK to me.

I believe what Stapel was getting at was more on the lines of:

g+c=15

19.3g+9c=238

You can do it this way. Truthfully, it's a better way. Simpler and more efficient than my method(my method solved for grams, hers in cc's). Always remember 'Occam's razor': in a nutshell, the simplest method is usually the best way to go.
 
ahhhhhhhhh! I understand now! This way, I get that c=5. This make a lot of sense too! THANK YOU EVERYONE FOR YOUR HELP!
 
You must log in or register to reply here.
Top