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# Each of the 30 first graders in a class bought one of three

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Joined: 10 Feb 2011
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Kudos [?]: 175 [0], given: 10

Each of the 30 first graders in a class bought one of three [#permalink]

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09 Mar 2011, 15:04
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Question Stats:

50% (00:00) correct 50% (00:40) wrong based on 2 sessions

269. Each of the 30 first graders in a class bought one of three kinds of dictionaries, pocket edition, at price of $15; compact edition, at price of$18; and ordinary edition, at price of $20. How many students bought the compact edition? (1) The total cost of all dictionaries bought by the students is 540 dollars. (2) The students who bought pocket edition are twice as many as the students who bought the compact edition. Intern Status: Sophomore Affiliations: President of Student Associoation Joined: 09 Dec 2010 Posts: 37 Schools: HBS 2+2, IESE YTP Followers: 1 Kudos [?]: 0 [0], given: 11 Re: 269. Each of the 30 first graders in a class bought one of t [#permalink] ### Show Tags 09 Mar 2011, 16:57 banksy wrote: 269. Each of the 30 first graders in a class bought one of three kinds of dictionaries, pocket edition, at price of$15; compact edition, at price of $18; and ordinary edition, at price of$20. How many students bought the compact edition?
(1) The total cost of all dictionaries bought by the students is 540 dollars.
(2) The students who bought pocket edition are twice as many as the students who bought the compact edition.

(2) let the number of students who bought the compact ed.=x,
the number of students who bought pocket ed.=2x
(1) 15*2x+18*x+20*y=540 and 2x+x+y=30 => 3x+y=30
y=15, x=5
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Re: 269. Each of the 30 first graders in a class bought one of t [#permalink]

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09 Mar 2011, 21:13
PE + CE + OE = 30

15 * PE + 18 * CE + 20 * OE = 540

From (1)

15 (30 - CE - OE) + 18 * CE + 20 * OE = 540

450 - 15CE - 15OE + 18CE + 20OE = 540

5OE + 3CE = 90

5 * 15 + 3 * 5 = 90, so PE = 10 and Total = 15* 10 + 18 * 5 + 20 * 15 = 150 + 90 + 300 = 540

5 * 9 + 3 * 15 = 90, so PE = 6 and Total = 15 * 6 + 18 * 15 + 9 * 20 = 90 + 270 + 180 = 540

Not enough

From (2)

PE = 2CE

2CE + CE + OE = 30

=> 3CE + OE = 30

CE can be 3, OE = 21, PE = 6

or CE can be 1, OE = 27, PE = 2

Noe enough

From 1 and 2 :

5OE + 3CE = 90
3CE + OE = 30

so OE = 15 CE = 5, and PE = 10

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Re: 269. Each of the 30 first graders in a class bought one of t   [#permalink] 09 Mar 2011, 21:13
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