Solve percent mixture problem using a linear equation

Question

In the lab, Elsa has two solutions that contain alcohol and is mixing them with each other. She uses
3
times as much Solution A as Solution B. Solution A is
13%
alcohol and Solution B is
18%
alcohol. How many milliliters of Solution B does she use, if the resulting mixture has
342
milliliters of pure alcohol?

Answer 1

Let x = the amount of Solution B used

 

3x = the amount of Solution A used

 

Realizing that 13% = 0.13 and 18% = 0.18, we can form the following equation:

 

3x(0.13) + x(0.18) = 342 (Remember, pure alcohol would have a concentration of 100% = 1.00)

 

0.39x + 0.18x = 342

 

0.57x = 342

 

x = 600 mL

 

Elsa uses 600 mL of solution B and 3(600) = 1800 mL of Solution A