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An empty mental box weights 10 percent of its total weight

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Senior Manager
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An empty mental box weights 10 percent of its total weight [#permalink] New post 13 Nov 2006, 13:39
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A
B
C
D
E

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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
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 [#permalink] New post 13 Nov 2006, 14:15
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
Senior Manager
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 [#permalink] New post 13 Nov 2006, 14:45
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
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 [#permalink] New post 13 Nov 2006, 14:53
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
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 [#permalink] New post 14 Nov 2006, 04:49
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 – 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%
  [#permalink] 14 Nov 2006, 04:49
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An empty mental box weights 10 percent of its total weight

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