Let x equal the number of liters of 40% solution, because that is the unknown value we want to find.
We can write the equation as follows (I'm writing the percentages as decimal values - e.g. 40% = 0.4)
(x)(0.4) + (8)(0.7) = (x+8)(0.5)
The total number of liters of solution (x+8) is the sum of the two individual amounts (x liters of 40% and 8 liters of 70%)
Multiply the values together and distribute the 0.5 into the parentheses on the right:
0.4x + 5.6 = 0.5x + 4.0
Subtract 0.4x from both sides to get all the terms with an x on the right side:
0.4x - 0.4x + 5.6 = 0.5x - 0.4x + 4.0
5.6 = 0.1x + 4.0
Subtract 4.0 from both sides to get all the constant terms on the left side:
5.6 - 4.0 = 0.1x + 4.0 - 4.0
1.6 = 0.1x
Divide both sides by 0.1 to get x by itself:
1.6/0.1 = (0.1x)/0.1
16 = x
So you need 16 liters of the 40% solution.
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