Blackbox wrote:
Bumping up and asking for a different explanation. So, according to
MGMAT's explanation, they used a table method to solve this question - which is not very helpful. Could someone explain in a simpler way to solve this using the table method? Also, isn't there "one ring to rule them all" for this type of questions?
p.s.: Sadly,I can't attach a screen grab of their explanation to this reply
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% 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?
A) 40%
B) 45%
C) 50 %
D) 60 %
E) 55 %
Yes there is a simple method :
Consider the following method
Brand A : 40% millet and 60% sunflower
Brand B : 65% millet and 35% safflower
Mix : 50% millet
Here the weighted average is 50%,
Now Brand A has 40% millet, which is 10% less than the weighted average of mix = - 0.10 A --------------- I
Similarly, Brand B has 65 % millet, which is 15 % more 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 = 60 %
Here is a pictorial representation :
Brand A= 40%------------------------10% or 0.10 below average, A times
-----------------Total below = - 0.10 A
---------------------------------------------------------------------------------------- Average = 50% or 0.50
Brand B = 65 %
--------------------------15% or 0.15 above 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 BA/B = 3/2
A:B: Total = 3:2:5 Therefore
A/Total = 3:5 = 60 %