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A certain used-book dealer sells paperback books at 3 times dealer's

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A certain used-book dealer sells paperback books at 3 times dealer's [#permalink]

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New post 23 Nov 2015, 12:36
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A certain used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times dealer's cost. Last week the dealer sold a total of 120 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus dealer's cost) on the sale of all of these books was $300, how many of the books sold were paperbacks?

(A) 40
(B) 60
(C) 75
(D) 90
(E) 100

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Re: A certain used-book dealer sells paperback books at 3 times dealer's [#permalink]

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New post 23 Nov 2015, 21:41
Selling price of paperback books = 3x
Selling price of hardback books = 4y
Total cost price = x + y = 120*1 = 120 ---- (1)
Profit = 300
Selling price = 3x + 4y = 120 + Profit = 420 --- (2)

(2) - 3*(1) --> y = 60
x + y = 120; x = 60

Answer: B
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Re: A certain used-book dealer sells paperback books at 3 times dealer's [#permalink]

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New post 23 Nov 2015, 23:05
Bunuel wrote:
A certain used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times dealer's cost. Last week the dealer sold a total of 120 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus dealer's cost) on the sale of all of these books was $300, how many of the books sold were paperbacks?

(A) 40
(B) 60
(C) 75
(D) 90
(E) 100


Hi,
the other way could be
the profit is 2 and 3 in the two cases..
if all were purchased of one kind the profit would be..
1) 240 (2*120) incase of paperbacks..
2) 360 (3*120) incase of the other..

actual profit= 300..
we can take the weighted avg but can straightway see that the actual is right in center of the two values.
so each type have equal numbers=120/2=60..
ans B
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Re: A certain used-book dealer sells paperback books at 3 times dealer's [#permalink]

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New post 06 May 2017, 01:39
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Let's assume the number of Paperbacks to be 'x' and the number of hardcovers to be 'y'.
So, the total number of books would be:
x+y=120 -- Eqn. 1

Now, for 'x' number of paperbacks costing him $1 each, his selling price according to the question would become '3x' and hence the profit would be '2x'.
Likewise, the selling price of hardcovers would become '4y' and the profit would be '3y'.
Now, we've been given that the profit is 300 i.e.
2x+3y=300 -- Eqn 2

On solving the above two equations, you'll get x and y to be 60 each.

Hope it helps :)
Re: A certain used-book dealer sells paperback books at 3 times dealer's   [#permalink] 06 May 2017, 01:39
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