Expert please help me solve this problem using alligation method, thanks!
Each female student at college class has 3 pens and 1 pencil. Each male student has 1 pen and 2 pencils. If the average number of pencils in the class is 1.4, what is the average number of pens?
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Mixture problem using alligation method
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Frankenstein
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Hi,
Pencils: Female - 1, Male - 2, Average - 1.4
Using alligation method, Ratio of males to females = (1.4-1)/(2-1.4) = 2:3
Pens: Female - 3, Male - 1
So, average number of pens = (1*2 + 3*3)/(2+3) = 11/5 = 2.2
(or)
Let Average be x
Using alligation method, Ratio of males to females = (3-x)/(x-1). We know that this ratio is 2:3
So, (3-x)/(x-1) = 2/3 => 9-3x = 2x-2 => x = 2.2
Pencils: Female - 1, Male - 2, Average - 1.4
Using alligation method, Ratio of males to females = (1.4-1)/(2-1.4) = 2:3
Pens: Female - 3, Male - 1
So, average number of pens = (1*2 + 3*3)/(2+3) = 11/5 = 2.2
(or)
Let Average be x
Using alligation method, Ratio of males to females = (3-x)/(x-1). We know that this ratio is 2:3
So, (3-x)/(x-1) = 2/3 => 9-3x = 2x-2 => x = 2.2
Cheers!
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GMATGuruNY
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Women = 1 pencil per woman.Redhorsep wrote:Expert please help me solve this problem using alligation method, thanks!
Each female student at college class has 3 pens and 1 pencil. Each male student has 1 pen and 2 pencils. If the average number of pencils in the class is 1.4, what is the average number of pens?
Men = 2 pencils per man.
Mixture = 1.4 pencils per person.
According to alligation:
The proportion of each element in the mixture is equal to the distance between the average attributed to the other element in the mixture and the average attributed to the mixture.
Proportion of women = |average in men - average in mixture| = |2 - 1.4| = .6
Proportion of men = |average in women - average in mixture| = |1 - 1.4| = .4
Ratio of women:men = 6:4 = 3:2.
3 women with 3 pens each = 3*3 = 9 pens.
2 men with 1 pen each = 2*1 = 2 pens.
Total number of pens = 9+2 = 11.
Total number of people = 3+2 = 5.
Total pens/Total people = 11/5 = 2.2.
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Followed here and elsewhere by over 1900 test-takers.
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.
For more information, please email me (Mitch Hunt) at [email protected].
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