Did I Understand the 18-karat Gold Problem Wrong?

[PascalPanther]

I thought I understood this problem, but my answer is wrong.

"In a sample of 18-karat gold, 75 percent of the total mass is pure gold, while the rest is typically 16 percent silver and 9 percent copper. If the density of pure gold is 19.3 g/cm^3, while the densities of silver and copper are respectively 10.5 g/cm^3 and 8.90 g/cm^3, what is the overall density of this alloy of 18-karat gold?"

So I understand that 18-karat gold is 75% gold because it is 18 parts out of 24, with the other 6 parts made up of silver and copper, equaling 100%. So it made sense to me, to do this:
Gold: (0.75)(19.3 g/cm^3) = 14.475 g/cm^3
Silver: (0.16)(10.5 g/cm^3) = 1.68 g/cm^3
Copper: (0.09)(8.9 g/cm^3) = 0.801 g/cm^3
Then I added them: 16.96 = 17.0 g/cm^3

This is wrong, isn't that what it is asking for? Did I understand the question wrong?

 

[Fermat]

75% of the mass is gold, but you have been working with 75% of volume.

 

[kyle8921]

I can confirm that your understanding of the 18-karat gold problem is correct. However, there may have been a calculation error in your answer. When adding the densities of gold, silver, and copper, the correct answer should be 16.956 g/cm^3, not 17.0 g/cm^3. This small difference may have led to your incorrect answer. It is also important to note that the overall density of this alloy of 18-karat gold is not exactly 16.96 g/cm^3, but rather a more precise value of 16.956 g/cm^3. Therefore, it is crucial to be precise in calculations when dealing with scientific problems. I suggest double-checking your calculations and also verifying the accuracy of the given densities to ensure the correct answer.