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# A diet contains 300 grams of a mixture of two foods, food X

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A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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20 May 2003, 11:49
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70% (02:50) correct 31% (02:03) wrong based on 400 sessions

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A diet contains 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 a diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?

(A) 150
(B) 145
(C) 100
(D) 160
(E) 140
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jul 2012, 08:11, edited 1 time in total.
Edited the question and added the OA.
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20 May 2003, 21:08
1.... 10/100*X + 15/100*Y = 38 (protein)

2.... X + Y = 300 (Total Mix)

Solve for X = 140
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20 May 2003, 21:53
Thanks a lot. I think i did some silly mistake while solving the equation for the first time.
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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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30 Jul 2012, 07:52
ju_1 wrote:
A diet contains 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 a diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?
(A) 150
(B)145
(C) 100
(D) 160
(E) 140

x(10%) y(15%)
38%
23% 28%

the protein parts in the final mixture for X:Y::23:28

hence

23 X
----------- = --------------
(23+28) 300

23/51 = x/300

x = 23 * 300
------------
51

hence x is approximately equal to 139.8

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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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30 Jul 2012, 08:13
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harshavmrg wrote:
ju_1 wrote:
A diet contains 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 a diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?
(A) 150
(B)145
(C) 100
(D) 160
(E) 140

x(10%) y(15%)
38%
23% 28%

the protein parts in the final mixture for X:Y::23:28

hence

23 X
----------- = --------------
(23+28) 300

23/51 = x/300

x = 23 * 300
------------
51

hence x is approximately equal to 139.8

Keep it simple: $$0.1x+0.15(300-x)=38$$ --> $$x=140$$ (exactly).

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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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13 Aug 2012, 00:41
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X contains 30 gms of protein (10% of 300 gms)
Y contains 45 gms of protein (15% of 300 gms)
Resultant mixture contains 38 gms of protien.

using scale method :

____8___________7___
30 38 45
w1 w2

therefore,
w1/w2 = 7/8

7x+8x=300 gms
=> x=20

so, w1 = 7x=7(20) = 140 gms
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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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13 Oct 2013, 13:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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18 Apr 2014, 22:12
X+Y = 300

0.1X + 0.15Y = 38

X=140
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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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04 Jul 2015, 07:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A diet contains 300 grams of a mixture of two foods, food X   [#permalink] 04 Jul 2015, 07:53
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