Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?

Question

In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 73.9 grams. I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml. Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?

Answer 1

First, divide your mass by your volume to get g/ml of the chain:

73.9 / 5 = 14.78 g/ml

 

Now you can compare your g/ml across all three.

 

14.78 g/ml = (x)(19.3 g/ml) + (y)(9.7 g/ml)   Where 'x' = % of gold and 'y' = % of other

 

Since you have 2 unknowns, you need two formulas.  As we are dealing with percentages, ie "parts of the whole", you can use:

x + y = 1  (1 is the decimal equivalent of 100%)

so y = 1 - x

 

Now, substitute (1-x) for y in the first equation and solve for x.  Then use your answer in the second equation and solve for y.

 

You should get two decimals.  Multiply by 100 to get the %

 

Hope that helps.