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