I have an algebra question

Question

in the lab, Omar has two solutions that contain alcohol and is mixing them with each other. he uses 4 times as much solution A as solution B. solution A is 16% alcohol and solution B is 13% alcohol. how many milliliters of solution B does he have if the resulting mixture has 539 milliliters of pure alcohol?

Answer 1

Our solution has a pure alcohol volume of 539 mL. It is comprised of mixing solution A with solution B. Therefore:

 

x mL * 0.16 + y mL * 0.13 = 539 mL

 

where x is the amount of solution A added and y is the amount of solution B added.

 

We are told that we used 4 times the amount of solution A as we did solution B. Therefore:

 

4y = x

 

By substitution, we have:

 

4y *0.16 + y * 0.13 = 539

0.64y + 0.13y = 539

0.77y = 539

700 = y

 

We used 700 mL of solution B.