SOLUTION: A plant food is to be made from three chemicals. The combined amounts of the first two chemicals must be 80% of the resulting mix. The second and third chemical must be in the rati

Question 708648: A plant food is to be made from three chemicals. The combined amounts of the first two chemicals must be 80% of the resulting mix. The second and third chemical must be in the ratio 4 to 3 by weight. How much of each chemical is needed to make 700 kg of the plant food?
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
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 .
The 80% requirement gives,
The ratio information indicates, .

Rework the last two equations into these:
, and .

The system of equations to work with then is this one:

Matrix operations is the way to continue here, at least partly.
That system can give us this matrix:

I briefly list the row operations but not here show the work.
, immediately giving .
, giving 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:

ANSWER: , , , all in pounds.
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