Propositiones - Part 1 - Answer

I presented the problem for Part 1 here.  The answer is as follows.

The merchant would need to buy 1 boar, 9 sows, and 90 piglets.  As there are three variables and only two equations, trial and error must be employed.  My solution is as follows.

X=Number of Boars
Y=Number of Sows
Z=Number of Piglets

[Eq 1]  X+Y+Z = 100
[Eq 2] 10X+5Y+0.5Z = 100

Solving Equation 1 for Z and substituting into Equation 2 and simplifying you get the following equation.

[Eq3] 1.9X + 0.9Y = 10

This is where trial and error comes in and you get X=1, Y=9.  Back substituting into Equation 1, you get that Z=90.

Hope you had fun!