If have this information....?

Question

what would the general form(x=(x,y,z)) of a bottle that can be made from these two sources
North End manufactures bottles from the mixture: 92% white glass, 6% brown glass, and 2% green glass
West Sidemanufactures botlles mixture: 70% white glass, 20% brown glass, and 10% glass.

Answer 1

We should take linear approximation: x2=a*k+x1; y2=b*k+y1; z2=c*k+z1, where x is for white, y is for brown and z is for green glass percentage, while 0<=k<=1 and a, b and c to be found.
If k=0 the system must give mixture x1=92, y1=6, z1=2; if k=1 then x2=70, y2=20, z2=10;
Thus 70=a*1+92 or a=-22, 20=b+6 or b=14, 10=c+2 or c=8;
All possible mixtures produced in between are:
X=-22k+92
Y=14k+6
Z=8k+2, being x+y+z=100 for any 0<=k<=1;
Thus if you want x be 85%, you must find k, that is 85=-22k+92, hence k=7/22=0.318;
This means you have to take 31.8% of mixture#1, the rest 68.2% being mixture#2;

Answer 2

the pure glass