SOLUTION: Ten liters of a 4% acid solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Question 969598: Ten liters of a 4% acid solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
5 liters ANSWER
Let x=liters of 10% solution.
10 liters * 0.04 (4%)acid= 0.4 acid-liters (it's a strange unit, but stay with me)
x liters * 0.10 (10%) acid= 0.1x acid-liters
I want a 6% solution (.06 acid) amount is 10+x liters (10 from 4%, x from 10%)
(10+x) liters *.06%=0.06(10-x) acid-liters
Let's distribute that to get 0.6-0.06 x
Now add the first two solutions and let them equal the third
0.4 a-l +0.1x a-l=0.6 a-l-0.06x a-l
subtract 0.4 a-l from each side
0.1 x a-l=0.2 a-l +0.06x a-l
Subtract 0.06 a-l from each side
0.04x a-l=0.2 a-l
divide by 0.04 the units are acid only, so we will be left with liters as the units, which is what we want.
x=5 liters.
Let's see if this works
10 *(0.04) + 5 (.10)=.4 +.5=0.9 I am multiplying liters times per cent acid for the two.
15*(0.06)=0.9 This is the final solution.
That checks

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