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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dividing 1000/15
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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.
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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Last edited by mattnyc15 on Sun Oct 25, 2015 9:46 am, edited 1 time in total.
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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
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
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GMATGuruNY
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I believe that the solution above refers to the following problem:
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
A's millet percentage: 40%.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?
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
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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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.
(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.
