Question

A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 5 milliliters of compound B. If a chemist wants to make 576 milliliters of the drug, how many milliliters of compound A are needed?

Answer 1

216 milliliters of compound A are needed.

Explanation:

There are two unknowns for the constituents of the final 576 milliliters of the drug:

amount of compound A (which we name A), and

amount of compound B (which we name B)

So we know two things that can be written in equation form;

1) there are 3 milliliters of A every 5 milliliters of B:

`(B)/(A) =(5)/(3) \\B=(5)/(3)\,A`

2) the chemist mixes 576 milliliters of the drug:

`A\,+\,B\,= 576`

So we now replace B with its expression in terms of A (from our first equation) in the second equation, and solve for A:

`A\,+\,B\,= 576\\A\,+\,(5)/(3) A=576\\(8)/(3) \,A=576\\A=(576\,*\,3)/(8) \\A=216`

So 216 milliliters of compound A are needed.