.
I just solved and answered this problem at the link
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1102280.html
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1102280.html
For your convenience, I copy and paste this solution here again:
-------------------------------------------
Below is your input with my editing:
Specific gravity of gold: 
19.259.
Specific gravity of quartz: 
2.652.
Determine ounces of gold in an mass of 210 oz. of both, the specific gravity is 
4.562.
Specific gravity is the weight of a volume of a substance divided by the weight of the same 
volume of water.
Water weighs 62.5 lbs. per cu. ft. <<<---=== In my solution I do not need this info.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
First step is to find the fraction "x" of the gold in 210 oz. of mixture of the specific gravity 4.562.
For it, use the density equation
x*19.259 + (1-x)*2.652 = 4.562.
19.259x + 2.652 - 2.652x = 4.562 ====> 16.607x = 4.562 - 2.652 = 1.91 ====> x = 
= 0.115.
So, the mass fraction of the gold in the mixture is 0.115.
Next step determine the mass of the gold in the mass of 210 oz of the mixture:
gold mass = 0.115*210 = 24.15 oz.
Answer. The mass of the gold is 24.15 oz.
Solved.
