A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 765 milliliters of the drug, how many milliliters of compound A are needed?

What is required to solve this is a basic idea or knowledge of the principle of ratios. According to the question, 5 millilitres of compound "A" must go together with 4 millimeters of compound "B" for every unit of the drug that must be produced.

This means that 5 millilitres of compound A will always go together with 4 millimeters of compound B.

Similarly 10 millilitres of A will require 8 millilitres of B.

Again, 15 millilitres of A must go together with 12 millilitres of B and so on.

Consider the case of having 10 millilitres of "A" which must go with 8 millilitres of B, totalling a combined quantity of 18 millilitres.

Assuming we do not know the different quantities of "A" and "B" that resulted in the combined quantity of 18 millilitres; if we know that A and B must ALWAYS be in the ratio 5:4 respectively, we can always figure out the different quantities of A and B in the drug.

Quantity of A = [5/(5+4)] × 18

= 5/9 × 18

= 10 ml.

Qty of B = [4/(5+4)] × 18

= 4/9 × 18

= 8ml.

We can apply this method to the 765ml drug that the chemist wants to make.

Since A and B are still in the ratio of 5:4 respectively, Then the quantity of compound A that is required is:

[5/(5+4)] × 765

= 5/9 × 765

= 425

Therefore the quantity of Compound "A" that is needed for the 765 millilitre drug is 425ml.