SOLUTION: 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 66.7 grams. I believe the chain is

Algebra ->  Systems-of-equations -> SOLUTION: 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 66.7 grams. I believe the chain is       Log On


   

Question 1159977: 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 66.7 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 by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.

Hey, water level IS NOT MEASURED in milliliters (!) (!) (!)
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This (or similar) problems go after Archimedes famous idea "Eureka ! --- Found (!)".

( see the links
https://www.scientificamerican.com/article/fact-or-fiction-archimede/
and
https://www.livescience.com/58839-archimedes-principle.html )


/\/\/\/\/\/\/\/\

Now see, how the problem SHOULD be formulated. 

    The alloy (gold and some other metal) has the volume of 5 cubic centimetres and the mass of 66.7 grams.


    The gold density is 19.3 g/cm^3, while the other metal's density is 9.7 g/cm^3.
    Determine what percentage of the alloy is gold, by mass, to at least 1 decimal place?


       +-----------------------------------------------------+
       |   All the rest in your formulation is bla-bla-bla   |
       |    with the only goal to confuse the reader . . .   |
       +-----------------------------------------------------+

Solution 

Let x be the mass of the gold in the chain and y be the mass of the other metal.


Then you have this system of 2 equations


    x + y = 66.7      (grams; the total mass)     (1)

    x%2F19.3 + y%2F9.7 = 5   (cm^3; the total volume)     (2)


Solve the system and get the answer.


            x +         y = 66.7        (3)

    0.051813x + 0.103093y =  5          (4)


Now, instead of solving manually, I will employ an online solver  www.reshish.com .


The answer it provides for x (the mass of gold) is 36.589 grams (with three decimals).


It is  36.589%2F66.7 = 0.549 part of the alloy by mass, or  54.9%    ANSWER

Solved.