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

Answer:

216 milliliters of compound A are needed.

Step-by-step 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:

$\frac{B}{A} =\frac{5}{3} \\B=\frac{5}{3}\,A$

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:

$A\,+\,B\,= 576\\A\,+\,\frac{5}{3} A=576\\\frac{8}{3} \,A=576\\A=\frac{576\,*\,3}{8} \\A=216$

So 216 milliliters of compound A are needed.