Question

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% millet, then what percent of mix is Brand A?
(a) 40
(b) 55
(c) 60
(d) 45

Answer 1

Hint: First, to calculate the answer easily and accurately we can set up a table and also assume that you have purchased a total of 100 lbs of brand A and assume the total quantity of Brand B as x lbs. Then, from the above table we get $ 40+0.65x=0.5\left( 100+x \right) $ and solve it to get the value of x. Then, to get the value of Brand A in the total mixture we have $ \dfrac{100}{100+\dfrac{1000}{15}} $ which gives the final percentage.

Complete step-by-step answer:
In this question, we are supposed to find the percentage of the Brand A in the mixture of millet and sunflower where millet is 50%.
So, before proceeding for this, we must know the situation which is a weighted average problem.
Now, to calculate the answer easily and accurately we can set up a table and also assume that you have purchased a total of 100 lbs of brand A.
Also, we can assume the total quantity of Brand B as x lbs.
Then, the distribution table can be made very easily to calculate the final answer.
So, the table after above assumption will be as:

Pounds(lbs)	Brand A	Brand B	Total
Millet	40	0.65x	0.5(100+x)
Sunflower	60	0.35x	0.5(100+x)
Total birdseed	100	X	100+x

Thus, from the above table we get:
 $ 40+0.65x=0.5\left( 100+x \right) $
Now, solve the above expression to get the value of x as:
 $ \begin{align}
  & 40+0.65x=0.5x+50 \\
 & \Rightarrow 0.65x-0.5x=50-40 \\
 & \Rightarrow 0.15x=10 \\
 & \Rightarrow x=\dfrac{10}{0.15} \\
 & \Rightarrow x=\dfrac{1000}{15} \\
\end{align} $
Now, to get the value of Brand A in total mixture we have:
 $ \dfrac{100}{100+\dfrac{1000}{15}} $
So, solve it to get the value of percentage of Brand A in following mixture:
 $ \begin{align}
  & \dfrac{100}{\dfrac{1500+1000}{15}}=\dfrac{100\times 15}{2500} \\
 & \Rightarrow \dfrac{1500}{2500} \\
\end{align} $
So, to get the percentage multiply it with 100, we get:
 $ \dfrac{1500}{2500}\times 100=60% $
So, Brand A is 60% of the total in the mixture
So, the correct answer is “Option C”.

Note: Now, to solve these types of questions we need to be careful in making assumptions as it will lead to wrong results. As, if we suppose the value of brand B as 100 lbs and solve according to it then it has been very difficult to solve because the condition is asked for brand A and also the percentage of millet matches with brand A only.