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# mixture 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?

I got 20 for an answer..this is what I did:
.15x+.6=.18x+.36
you said i was correct up to that point..then...i want to take 15x from both sides...gives me .6=.03x+.36
subtact .36 from both sides....divide both sides by .03 get 20

Karen,
you have .03x=.24  (.60-.36)  dividing both sides by .03 gives x=.24/.03 = 8 . How did you get 20?
Jim
Hi Jim...back to where I asked: 15x+6=.18x+36
now take 15x from both sides,yes? 6=.03x +36 yes?
now 36 from both sides? -30=.03x ?
where are you getting 24? did i state the problem wrong at the beginning...i am totally confused
from the top:
how many liters of a 15% solution must be added to 2 liters of a 30% solution to yield a 18% salt?

I started with: .15x = .30(2)or .6=x +2(18) and 2(x) which is: .15x+.6=.36 +x
15x +6= 18x +36...take 15x from both sides  now its .6=..03x +36...now take 36 from both sides...-30=.03x...what am i doing wrong?
Jim...I just slowed down and realized it was my addition/subtraction...thanks so much for your help and patience!
Karen
Karen,
No problem I made the same mistake first time around. .6-.34 is .24 :)
take care
jim
My biggest issues in Algebra have always been to slow down and check the math....positives/negatives!
Thanks again.

### 2 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
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
Jim S. | Physics (and math) are fun, reallyPhysics (and math) are fun, really
4.7 4.7 (189 lesson ratings) (189)
0
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