mixture question

Question

i keep doing this one over and over and i must be not setting it up correctly.help!

quesiton:how many liters of a 15% salt solution must be added to 2 liters of a 30% salt solution to yield a solution of 18%

 

this is what i did and the answers i am getting are not jiving..

First I set it up like this:    15%   x  .15 =.15x

                                       30%   2  .30 +.30(2)

                                      Mixture x+2 .18 =.18(x+2)

If this is correct I then get .15x +.6= .18(x+2)   .15x +6 = .18x +.36  combine like terms get rid of the .18x on both sides..so now its:-.03x +.6=.36 take .6 from both sides....24  now its .-03x = .24

divide both sides by -.03 to get 8

 

Answer 1

X - amount in liter of 15% solution 

 

X ( 0.15) + 2 ( 0.30) = ( 2 + x  )0.18

 

  0.15 X + 0.60 = 0.36 + 0.18X

 

   0.24  = 0.3 X

 

   X = 8 liter.

Answer 2

.15x +.6= .18(x+2) is right

You should get .03x = .24 (not negative .03x)

8 is the right answer.

 

Does this make sense? 18% much closer to 15% than 30%. So we need a much greater volume of the 15% solution. You answer 8L makes sense.