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# An empty mental box weights 10 percent of its total weight

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Senior Manager
Joined: 22 Sep 2005
Posts: 278

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An empty mental box weights 10 percent of its total weight [#permalink]

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13 Nov 2006, 14:39
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An empty mental box weights 10 percent of its total weight when filled with varnish. if the weight of a partly filled box is one-half taht of a completely filled box, what fraction of the box is filled?

A) 3/5

B) 5/9

C) 1/2

D) 4/9

E) 2/5

Kudos [?]: 244 [0], given: 1

Retired Moderator
Joined: 05 Jul 2006
Posts: 1749

Kudos [?]: 443 [0], given: 49

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13 Nov 2006, 15:15
An empty mental box weights 10 percent of its total weight when filled with varnish. if the weight of a partly filled box is one-half taht of a completely filled box, what fraction of the box is filled?

A) 3/5 B) 5/9 C) 1/2 D) 4/9 E) 2/5

let total weight when filled = x

when empty = .1x thus varnich = 0.9x

completely partly filled box = 0.5x

fraction filled = 0.5x - .1x = .4x= 2/5

my choice is E

Kudos [?]: 443 [0], given: 49

Senior Manager
Joined: 08 Jun 2006
Posts: 335

Kudos [?]: 63 [0], given: 0

Location: Washington DC

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13 Nov 2006, 15:45
I think we need to go one more step ahead...
Here we got the weight of the partly filled box = 2x/5
So the fraction is = partly filled weight / total weight = (2x/5)/(9x/10) = 4/9

Kudos [?]: 63 [0], given: 0

Director
Joined: 28 Dec 2005
Posts: 915

Kudos [?]: 59 [0], given: 0

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13 Nov 2006, 15:53
I get D:4/9
If x is total weight when box is full of varnish,

weight of box = x/10

if the fraction of the box that's full = 1/n, the weight of 1/nth of the box =

0.1x + 0.9x/n which is then = 0.5x

solving, we get 4/9

Kudos [?]: 59 [0], given: 0

Manager
Joined: 03 Jul 2005
Posts: 191

Kudos [?]: 12 [0], given: 0

Location: City

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14 Nov 2006, 05:49
An empty mental box weights 10 percent of its total weight when filled with varnish. if the weight of a partly filled box is one-half taht of a completely filled box, what fraction of the box is filled?

A) 3/5

B) 5/9

C) 1/2

D) 4/9

E) 2/5

W = W/2
WE = 0.1WF
WE + K = WF / 2
0.1WF + K = WF / 2
2K = WF â€“ 0.1WF
2K = 0.9WF
K = 0.9WF / 2
K = 0.45WF

Approx:
A = 15%
B = 55%
C = 50%
D = 44% CLOSED ANSWER D
E = 10%

Kudos [?]: 12 [0], given: 0

14 Nov 2006, 05:49
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