Question 885880
How much of the mix does the zoologist want?  Call this Q.


These are in grams:
x = how much of A
y = how much of B
z = how much of C


PROTEIN:  {{{0.20x+0.10y+0.15z=23}}}

FAT:  {{{0.02x+0.06y+0.05z=6.2}}}

MOISTURE:  {{{0.15x+0.10y+0.05z=16}}}


Three linear equation in three unknowns.  The simplification to do is multiply each equation's left and right members by 20.  That will ALMOST give the system of equations with whole number coefficients.


EQUIVALENT SYSTEM:
{{{4x+2y+3z=460}}}
{{{0.4x+1.2y+z=124}}}
{{{3x+2y+z=320}}}


Not quite simple enough..  Multiply the "124" equation by {{{(5/2)}}}


EQUIVALENT SYSTEM:
{{{4x+2y+3z=460}}}
{{{x+3y+z=310}}}
{{{3x+2y+z=320}}}


A possible way for Elimination is solve eq.2 for z and solve eq.3 for z.  This gives you two linear equations in x and y.  Solve THIS system for x and y.  Having the values now for x and y, use them (in equation 1) to solve for and find the value for z.


NOW you can solve the system either by Elimination Method or with matrix row operations.