I believe that the solution above refers to the following problem:

A feed store sells two varieties of birdseed: Brand A, which is 40% millet & 60% safflower; Brand B, which is 65% millet & 35% safflower. If a customer purchases a mix of two birdseed that is 50% millet, what % of the mix is Brand A?

A's millet percentage: 40%.
B's millet percentage: 65%.
Millet percentage in the mixture: 50%.

The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for A and B on the ends and the percentage for the mixture in the middle.
A 40%-----------50%-----------65% B

Step 2: Calculate the distances between the percentages.
A 40%----10-----50%----15-----65% B

Step 3: Determine the ratio in the mixture.
The required ratio of A to B is equal to the RECIPROCAL of the distances in red.
A:B = 15:10 = 3:2.

Since A:B = 3:2, every 5 pounds of mixture is composed of 3 pounds of A and 2 pounds of B.
Thus:
A/total = 3/5 = 60%.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

Another approach here:

(40% of A) + (65% of B) = (50% of A and B)

.4A + .65B = .5(A+B)

.4A + .65B = .5A + .5B

.15B = .1A

15B = 10A

3B = 2A

3/2 = A/B

So the mixture is three parts A and two parts B, meaning that A = 3 of the 5 parts, or 60% of the mix.