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

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Each of the 30 first graders in a class bought one of three [#permalink] New post 09 Mar 2011, 14:04
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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.
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Re: 269. Each of the 30 first graders in a class bought one of t [#permalink] New post 09 Mar 2011, 15:57
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
Answer C.
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Re: 269. Each of the 30 first graders in a class bought one of t [#permalink] New post 09 Mar 2011, 20:13
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

Answer is C
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Re: 269. Each of the 30 first graders in a class bought one of t   [#permalink] 09 Mar 2011, 20:13
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Each of the 30 first graders in a class bought one of three

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