Question #4ede0

1 Answer
Dec 17, 2014

The answer is 3:1 in favor of the 20% solution.

I'll show you two ways of doing this, an easy one and an easier one.

The easiest way of solving this problem is by setting up 2 equations

a * 20 + b * 60 = 30 and
a + b =1

SInce we're dealing with mass ratios, we'll assume that the final solution has a fraction a of the 20% solution and a fraction b of the 60% solution; a + b must be equal to one since we're dealing with fractions of a total.

Now, solving the system of equations will produce

a = 1-b -> 20(1-b) + 60b = 30 -> 40b = 10 -> b = 1/4

And a = 1-b = 3/4

So your solution needs 3/4 of the 20% solution and 1/4 of the 60% solution; therefore, the mass ratio between the two solutions is 3:1.

The second way of doing this is by using the rule of the cross

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You start by placing the starting concentrations on the top row - 20% on top-left, 60% on top-right; you place the desired concentration in the middle - 30%.
Then you substract according to the BLACK lines to get the parts of each solution needed to make the desired one. So,

30 - 20 = 10, and 60 -30 = 30

The final solution will have 30 + 10 = 40 parts, out of which

10 parts -> 60% solution - follow the BLUE line on the right;
30 parts -> 20% solution - follow the BLUE line on the left;

So, once again, the mass ratio between the two solutions will be 3:1 for the 20% solution.