Question

Question #4ede0

Answer 1

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

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.