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The Question:

Different types of solder are alloys of different proportions of copper, tin and lead. The specific gravity of tin copper and lead are 8, 6 and 14 respectively while the specific gravities of three different solders are 9.6, 9.7 and 9.1.

Find the percentage composition of each solder.

The Issue:

I do not understand how it is possible to use the specific densities of the metals to find the densities of the solders as there are more variables than there are equations that can be formed (as far as I can decern).

Additionally, it may be helpful to know that this is a question from a chapter focused on Gaussian elimination.

Any help would be appreciated.

REnt12
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  • You have posted two questions that appear to come from the same text. Both of them are underspecified. If you haven't left out important information, complain to the author. – Ross Millikan Nov 18 '17 at 15:47

1 Answers1

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The unstated assumption is that the volume of the mix is the sum of the volumes of the components. The densities are in g/cm^3. Under this assumption, if you mix $x$ grams of copper, $y$ grams of tin, and $z$ grams of lead the volume of the product will be $\frac x8+\frac y6+\frac z{14}$, so the specific gravity of the product will be $\frac {x+y+z}{\frac x8+\frac y6+\frac z{14}}$. For the first mix we have to solve $\frac {x+y+z}{\frac x8+\frac y6+\frac z{14}}=9.6$ This looks like one equation in three unknowns, but you can eliminate one because you can specify the total amount you make. That still leaves you with one extra unknown and there is not a unique solution.

Ross Millikan
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