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Mixture problem using alligation method

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Mixture problem using alligation method

by Redhorsep » Thu Aug 18, 2011 2:24 pm
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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by Frankenstein » Thu Aug 18, 2011 7:57 pm
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
Cheers!

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by blackjack » Fri Aug 19, 2011 5:22 am
Is there another way to solve this?
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by GMATGuruNY » Fri Aug 19, 2011 5:32 am
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?
Women = 1 pencil per woman.
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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