In chemistry class, 6 liters of a 4% sliver iodide solution must be mixed with a 10% solution to get a 6% solution how many liters of the 10% solution is needed?

Let's focus on how much silver iodide we have and how much we obtain.

6 liters of a 4% solution constitutes 6(0.04) liters of silver iodide:

0.24 liter.  Let x be the number of liters of the 10% solution.  The amount of silver iodide in that is 0.10(x).

Adding together these two volumes of silver iodide:

0.24 liter + 0.10x = 0.06(6 + x) liters

Then 0.24 + 0.10x = 0.36 + 0.06x

Simplifying, 0.04x = 0.12.  Dividing both sides by 0.04, x = 0.12/0.04 = 3

3 liters of the 10% solution are needed in order to end up with a 6% solution of silver iodide.

Check:  0.04(6) + 0.10(3)  = ? 0.06(6+3)
0.54 = ? = 0.06(9)
0.54 = ? = 0.54   Yes.  So, our result is correct.