Question 1159977
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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 )



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Now see, how the problem SHOULD be formulated.


<pre>
    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 . . .   |
       +-----------------------------------------------------+
</pre>

<B>Solution</B>


<pre>
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/19.3}}} + {{{y/9.7}}} = 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  {{{36.589/66.7}}} = 0.549 part of the alloy by mass, or  54.9%    <U>ANSWER</U>
</pre>

Solved.