Mixture Problem where Only Very Few Information is Known

by Yohanes Nuwara   Last Updated June 12, 2019 07:20 AM

Help me on this. This is an advanced mixture problem for me.

Assuming a rock has four mineral compositions (fraction), that the percentage is unknown. Only density of the minerals are known. Density of mineral A = 2.71 g/cc, mineral B = 2.58 g/cc, mineral C = 2.87 g/cc, and mineral D = 2.65 g/cc. The rock has density of 2.72 g/cc.

How much percentage of minerals in the rock? The equation of rock density is:

RockDensity=(Fraction_A x Density_A)+(Fraction_B x Density_B)+(Fraction_C x Density_C)+(Fraction_D x Density_D)

Therefore:

2.72=(Fraction_A x 2.71)+(Fraction_B x 2.58)+(Fraction_C x 2.87)+(Fraction_D x 2.65)

How much fraction of each mineral in these rocks if only this information is known??? Fractions can be any, so when you input the fractions into the equation, you will come up with a new calculated RockDensity. But, the difference or misfit between calculated RockDensity and real RockDensity must be 1% (tolerable error).

This is a kind of inverse problem, perhaps least square inversion method can solve this. But I come to a stuck. Is there any fast way to compute these fractions?

Thanks a lot :)

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