A feed store sells two varieties of birdseed: Brand A, which is 65% millet and 35% sunflower, and Brand B, which is 40% millet and 60% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?	Choose the correct choice:  A) 40%  B) 45%  C) 50 %  D) 60 %  E) 55 %
Yes there is a simple method :   Consider the following method   Brand A : 65% millet and 35% sunflower   Brand B : 40% millet and 60% safflower   Mix : 50% millet   Here the weighted average is 50%,   Now Brand A has 65% millet, which is 15% more than the weighted average of mix = + 0.15 A --------------- I   Similarly, Brand B has 40 % millet, which is 10 % less than the weighted average of mix = - 0.10B ------------ II   Now, both Brand A and Brand B are combined to give a 50% mix containing millet, so equate I and II   implies, 0.15 A = 0.10 B   Therefore A/B = 0.10/0.15 = 2/3   A : B : (A + B) = 2 : 3 : (3+2) = 2 : 3 : 5   We have to find, percent of the mix is Brand A i.e. 40% : (40% + B) = 2 : 5 = (2 / 5) * 100= 
<gadget id="calculator">(2 / 5) * 100</gadget>
<output>40</output>
40 %   Here is a pictorial representation :   Brand 40%= 65%------------------------15% or 0.15 above average, 40% times-----------------Total below = + 0.15 40%   ----------------------------------------------------------------------------------------40%verage = 50% or 0.50   Brand B = 40%--------------------------10% or 0.10 below average, B times-----------------Total above = - 0.10 B   Since the amount below the average has to equal the average above the average; therefore,   0.15 40% = 0.10 B   40%/B = 2/3   40%:B: Total = 2:3:5   Therefore   40%/Total = 2:5 = 40 %
<result>A</result>
A feed store sells two varieties of birdseed: Brand A, which is 65% millet and 35% sunflower, and Brand B, which is 40% millet and 60% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?