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# A school has only two classes - class X and class Y.

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Joined: 14 Sep 2005
Posts: 985
Location: South Korea
A school has only two classes - class X and class Y.  [#permalink]

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20 Dec 2005, 20:52
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A school has only two classes - class X and class Y.

Students in class X each have two pencils and one pen, and students in class Y each have one pencil and three pens. The average number of peicils each student has is 1.6.

What is the average number of pens each student has?
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Auge um Auge, Zahn um Zahn !

Senior Manager
Joined: 05 Oct 2005
Posts: 485
Re: PS - Average pens [#permalink]

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20 Dec 2005, 21:22
gamjatang wrote:
A school has only two classes - class X and class Y.

Students in class X each have two pencils and one pen, and students in class Y each have one pencil and three pens. The average number of peicils each student has is 1.6.

What is the average number of pens each student has?

Student in class X - 2 pencils, 1 pen
Student in class Y - 1 pencil , 3 pens

No. of students in class X = x
No. of students in class Y = y

(2x+y)/(x+y) = 1.6
2x+y = 1.6x + 1.6y
.4x = .6y
x/y = 3/2

Since we know the ratio, we know the proportion.

(1(3) + 3 (2))/(3+2) = 9/5 = 1.8

Avg. no. of pens = 1.8

By the way, gamgatang, thanks for posting these questions, they are very helpful in my prep.
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Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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20 Dec 2005, 22:38
X = 2 pencils, 1 pen
Y = 1 pencil, 3 pens

let number of students in class X be x, and number of students in class Y be y

(2x + y)/x+y = 1.6
2x+y = 1.6x + 1.6y
0.4x - 0.6y = 0
0.4x = 0.6y
x = 1.5y

ave number of pens = x + 3y/(x+y). Since x = 1.5y, so x + 3y/(x+y) = 4.5y/2.5y = 1.8 average number of pens
20 Dec 2005, 22:38
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