Fabio bought several pairs of socks, some woolen and the : DS Archive
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# Fabio bought several pairs of socks, some woolen and the

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Fabio bought several pairs of socks, some woolen and the [#permalink]

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14 Oct 2007, 05:23
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Fabio bought several pairs of socks, some woolen and the others cotton. The price of the each pair of woolen socks was \$3 higher than the price of each pair of cotton socks. What was the average price of the pairs of socks that Fabio bought?

(1) He bought three times as many pairs of cotton socks as woolen socks.
(2) He spent twice as much money on cotton socks as he did on woolen socks.
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14 Oct 2007, 06:29
Cotton socks price = x
Woolen socks price = x+3

Cotton socks amount = C
Woolen socks amount = W

statement 1

C/3 = W

C = 3W

insufficient

statement 2

Cx/2 = W(x+3)

Cx = 2Wx+6W

insufficient

both statements

C = 3W
Cx = 2Wx+6W

3Wx = 2Wx+6W

Wx = 6W

x = 6

6C/2 = W(6+3)

3C = 9W

C = 3W

sufficient

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14 Oct 2007, 08:38
price of cotton socks = x
price of woolen socks = x+3

1: number of woolen socks = n
number of cotton socks = 3n

so total exp = n(x+3) + 3n(x) = 4nx + 3n
avg price of the pair of the socks = (4nx + 3n)/(4n) = (4x+3)/4..nsf

2: total purchase price of woolen = w
total purchase price of cotton = c

total purchase price of cotton = 2 (total purchase price of woolen)
c = 2w

so no relation between c and w....

from 1 and 2:

c = 2w
x (3n) = 2 n (x+3)
3x = 2x+6
x = 6

total exp = 4nx + 3n
avg = (4nx + 3n)/(n+3n)
avg = (4x + 3)/4 = (4 * 6 + 3)/4 = 27/4=6.75

C.
14 Oct 2007, 08:38
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