prepare 30 ml of a 1:200 solution by combining a 1:10 and a 1:400 solution, how much of each is needed?

Let x = amount of 1:10 solution needed

then, 30 - x = amount of 1:400 solution needed

(1/10)x + (1/400)(30 - x) = (1/200)(30)

Multiply everything by 400 to get rid of the 400 in the denominator

40x + (30 - x) = 60

39x = 30

x = 30/39 = 10/13 = 0.77 ml of the 1:10 solution

30 - x = 30 - 0.769 = 29.23 ml of the 1:200 solution

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