Solving a percent mixture problem using a linear equation

Question

Ali has two solutions that contain alcohol and is mixing them with each other. Solution A is 7% alcohol and Solution B is 2% alcohol. He uses 600 milliliters of Solution A. How many milliliters of Solution B does he use, if the resulting mixture is a 5% alcohol solution?

Answer 1

Set up a weighted combination of the mixtures.

 

x = ml of solution B

 

(7%)(600 ml) + (2%)x = (5%)(x + 600 ml)

 

Solve for x.

 

4200 + 2x = 5x + 3000

 

1200 = 3x

 

x = 400 ml