mixture question

Question

How many liters of 15% salt solution must be added to 2 liters of 30% salt solution to yield a solution that is 18%?

I am setting it up as follows..is this correct?

15% (x )liters =.15x      30%(2liters)=.30(2)=.6

The mixture would be: x +2(18)= .18(x +2)= .18x +.36

So, .15x + .6= .18x +.36

Am I right so far?

Answer 1

 X - amount in liter of salt solution.

 

 X ( 0.15) + 2 ( 0.30) =( 2 + X) 0.18

 

  X ( 0.15) + 0.60 = 0.36 + X ( 0.18)

 

       0.24 = X ( 0.03) 

 

    X = 0.24/ 0.03 = 8 liter

Answer 2

Hi Karen,

 

     You are on the right track here, solving for x gives x=8 L. So if you take 8 L of the 15% solution and add it to the 2 L of 30% you will have 1.2 g + .6 g of salt which you are adding to 10 L (8+2) 1.2+.6 = 1.8g of salt in 10 L which is a (1.8/10)*100 =18% solution. QED

 

Jim