a 40%acid solution and a 70%acid solution are used to make 30 liters of a 60% acid solution.how many liters of the 40% acid solution are use

I think GL has, very sensibly, first considered a single unit:

0.4*x + 0.7*(1-x) = 1

-0.3x +0.7 = 1

-0.3x = -0.1

x = 1/3

so, with 30L you simply require (1/3)*30 L

No doubt GL considered the lead up to the final equation too obvious to be worth spelling out!!

Nope! I've just noticed the answer to http://web2.0calc.com/questions/a-10-acid-solution-and-a-70-acid-solution-are-used-to-make-15-liters-of-a-50-acid-solution-how-many-liters-of-the-70-acid-solution-are-u#r2 and GL does use guesswork!!

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More number-crunching. This time, it's gonna be two parts 70% solution and one part 40% solution. This one is really easy to figure out the numbers for, but just for you:

$${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{30}}\right) = {\mathtt{10}}$$

10 liters of 40% solution were used.

Where did your numbers come from Golden Leaf?  You need to show how you get your answers.

40% OF X + 70% OF Y = 60% OF (X+Y)

X+Y=30

Y=30-X

so

0.4X   +   0.7(30-X)   = 0.6*30

0.4X   +   21 - 0.7X   = 18

-0.3X   = -3

x          =-3/-0.3

       X  =  10

10ml of the 40% solution are needed. 

Melody......I tried to figure out GL's solution methods to these "solution" problems.....he must have "guessed and checked".......maybe he knows some easier method......!!!!