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 $35$% 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. 55
• C. 60
• D. 45

Answer 1

Answer: (C)

60

This is a weighted averages problem. You can set up a table to calculate the answer, and assume that you purchased $100$ lbs of Brand $A$:

Pounds (lbs)	Brand A	Brand B	Total
Millet	$40$	$0.65x$	$\left(0.5\right)(100+x)$
Other stuff	$60$	$0.35x$	$\left(0.5\right)(100+x)$
Total birdseed	$100$	$x$	$100+x$

Thus, $40+0.65x=\left(0.5\right)(100+x),40+0.65x=50+0.5x,0.15x=10,x=\frac{1,000}{15}$.
Therefore, Brand $A$ is $\frac{100}{100+\frac{1,000}{15}}=\frac{100}{\frac{1,500}{15}+\frac{1,000}{15}}=\frac{1,500}{2,500}=60$% of the total.