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:
[tex]\frac{B}{A} =\frac{5}{3} \\B=\frac{5}{3}\,A[/tex]
2) the chemist mixes 576 milliliters of the drug:
[tex]A\,+\,B\,= 576[/tex]
So we now replace B with its expression in terms of A (from our first equation) in the second equation, and solve for A:
[tex]A\,+\,B\,= 576\\A\,+\,\frac{5}{3} A=576\\\frac{8}{3} \,A=576\\A=\frac{576\,*\,3}{8} \\A=216[/tex]
So 216 milliliters of compound A are needed.
