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A rabbit

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Intern
Joined: 26 Feb 2011
Posts: 38
Followers: 1

Kudos [?]: 49 [0], given: 1

A rabbit [#permalink]  02 Mar 2011, 05:28
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If the rabbits diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?

A/ 100
B/ 140
C/ 150
D/ 160
E/ 200
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 272 [0], given: 123

Re: A rabbit [#permalink]  02 Mar 2011, 05:39
Let there be X and Y gm of food.
0.10 X + 0.15 Y = 38
or 10 X + 15 Y = 3800 -----(1)

X + Y = 300 ---------(2)
1) + 2) Eliminating Y, we get
X = 140 gm

A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If the rabbits diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?

A/ 100
B/ 140
C/ 150
D/ 160
E/ 200
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 272 [0], given: 123

Re: A rabbit [#permalink]  02 Mar 2011, 05:48
Alternately using the law of balances. The more the difference from the mean, the less the quantity.
38 gm is 38/300 or 38/3 %

X is 10%
Y is 15%
mean is 38/3 %.i.e. 10 < 38/3 < 15

Hence ratio of X : Y in mixture = (15 - 38/3) / (38/3 - 10) = 7 : 8
Hence X = 7/15 of 300 gm = 140 gm
SVP
Joined: 16 Nov 2010
Posts: 1675
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 32

Kudos [?]: 412 [0], given: 36

Re: A rabbit [#permalink]  02 Mar 2011, 08:16
Let x be the amount of Food X

0.1x + (300-x)0.15 = 38

-0.05x = 38-45

=> x = 140

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Re: A rabbit   [#permalink] 02 Mar 2011, 08:16
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