A feed store sells two varieties of birdseed: Brand $A,$ which is 40% millet and 60% sunflower, and Brand $B,$ which

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Wed May 20, 2020 6:02 am

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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 %

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT

Source: Beat The GMAT — Problem Solving | Wed May 20, 2020 6:02 am

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Re: A feed store sells two varieties of birdseed: Brand $A,$ which is 40% millet and 60% sunflower, and Brand $B,$ w

by Scott@TargetTestPrep » Mon Jun 01, 2020 7:18 am

VJesus12 wrote: ↑
Wed May 20, 2020 6:02 am
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 %

[spoiler]OA=D[/spoiler]

Solution:

We can let x = the amount of millet in Brand A and y = the amount of millet in Brand B. We can create the equation:

0.4x + 0.65y = 0.5(x + y)

40x + 65y = 50x + 50y

15y = 10x

3y = 2x

We see that we can let x = 3 and y = 2 (so that 3y = 2x). Thus, the percent of the mix that is Brand A is 3/(3 + 2) = 3/5 = 60%.

Answer: D

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