MATH HW HELP NEEDED

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 67.2 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

Hello Ariel,

From the setup of your problem we can find the density of the chain by simply dividing the mass of the chain to the volume displaced on the water by the chain. Once you find the density we can assume that the mass percent of gold will affect the denisty of the chain linearly, since the volume displaced by the chain is constant so the mass percent is the same of the denisty percent. If we assume that this chain is composed of 2 metals which is gold and some other metal, and we know the denisty of these two metals, then we can create an algebraic problem as such: (denisty of gold)*x + (denisty of other metal)*(1 - x) = density of chain, where * means multiply and x is the unknown mass percent of gold. Note that the mass percent of gold and the other metal that makes up the mass of the chain must add up to 100% or 1, so if we state that mass percent of gold is x then the mass percent of the other metal must be 100% - mass percent of gold = 100% - x = 1 - x