Question 708648
Use a, b, and c as the quantities each chemical.
These initial equations can be made from the problem description:

The total was to be 700 pounds, so {{{a+b+c=700}}}.
The 80% requirement gives, {{{(a+b)/700=0.8}}}
The ratio information indicates, {{{b/c=4/3}}}.


Rework the last two equations into these:
{{{a+b=560}}}, and {{{b-(4/3)c=0}}}.


The system of equations to work with then is this one:
{{{a+b+c=700}}}
{{{a+b=560}}}
{{{b-(4/3)c=0}}}


Matrix operations is the way to continue here, at least partly.
That system can give us this matrix:
{{{(matrix(3,4,1,1,1,700,
1,1,0,560,
0,1,-4/3,0
))}}}


I briefly list the row operations but not here show the work.
{{{R[1]-R[2]= R[2]}}}, immediately giving {{{c=140}}}.
{{{R[3]+(4/3)R[1]=R[3]}}}, giving b=186 2/3, {{{b=186&2/3}}}.


Now having b and c, the 700 summation equation can be used and b and c simply subsituted to find a (not continuing further with matrix operations).  
result for a:  {{{a=373&2/3}}}


ANSWER: {{{a=373&1/3}}}, {{{b=186&2/3}}}, {{{c=140}}}, all in pounds.