SOLUTION: A chemist mixes a 5% salt solution with an 11% salt solution. How many milliliters of each should be used to make 600 milliliters of a 7% salt solution?

In this problem, concentrations are the ratios of a salt mass (in grams) to the volume of a mixture (in milliliters).



Let x be the amount of the 5%  solution needed (in milliliters), and

let y be the amount of the 11%  solution needed.



The mass of the salt in the 5% mixture  is 0.05x grams.

The mass of the salt in the 11% mixture is 0.11y grams.

The resulting mixture contains  0.05x + 0.11y grams of the dissolved salt and has the volume of 600 mL.


Thus you have these two equations


    x + y = 600    milliliters           (1)    (the total volume)

     = 0.07.                 (2)    (the resulting mixture concentration)



From equation  (1), express  x = 600 - y.  Substitute it into equation (2) and multiply both sides of this equation by 600. 
You will get


    0.05*(600-y) + 0.11y = 0.07*600.


From the last equation express y and calculate


    y =  = 200 mL of the 11% mixture are needed.


Then from equation (1),  x = 600 - 200 = 400 mL of the 5% mixture are needed.


Answer. 200 mL of the 11% mixture  and  400 mL of the 5% mixture are  needed.


Check.   = 0.07 = 7%.   ! Correct concentration !