dividing 1000/15

[mattnyc15]

A feed store sells two varieties of birdseed: Brand A, which is 40% millet & 60% safflower; Brand B, which is 65% millet & 35% safflower. If a customer purchases a mix of two birdseed that is 50% millet, what % of the mix is Brand A?


Can someone please explain this rational of adding the 100 + 1,000/15 in the denominator? This is really confusing for some reason.

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Hi mattnyc15,

Can you post the original prompt that these screen captures are meant to explain? There is likely some type of 'clue' in the prompt that would help you to get through this solution.

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

I believe that the solution above refers to the following problem:

A feed store sells two varieties of birdseed: Brand A, which is 40% millet & 60% safflower; Brand B, which is 65% millet & 35% safflower. If a customer purchases a mix of two birdseed that is 50% millet, what % of the mix is Brand A?

A's millet percentage: 40%.
B's millet percentage: 65%.
Millet percentage in the mixture: 50%.

The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for A and B on the ends and the percentage for the mixture in the middle.
A 40%-----------50%-----------65% B

Step 2: Calculate the distances between the percentages.
A 40%----10-----50%----15-----65% B

Step 3: Determine the ratio in the mixture.
The required ratio of A to B is equal to the RECIPROCAL of the distances in red.
A:B = 15:10 = 3:2.

Since A:B = 3:2, every 5 pounds of mixture is composed of 3 pounds of A and 2 pounds of B.
Thus:
A/total = 3/5 = 60%.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

[Matt@VeritasPrep]

Another approach here:

(40% of A) + (65% of B) = (50% of A and B)

.4A + .65B = .5(A+B)

.4A + .65B = .5A + .5B

.15B = .1A

15B = 10A

3B = 2A

3/2 = A/B

So the mixture is three parts A and two parts B, meaning that A = 3 of the 5 parts, or 60% of the mix.