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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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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
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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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1.... 10/100*X + 15/100*Y = 38 (protein)
2.... X + Y = 300 (Total Mix)
Solve for 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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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 hence the answer is E
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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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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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18 Apr 2014, 22:12
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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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07 Aug 2016, 06:02
start with some numbers. if x = 100, then y=200 protien from x = 10 and from y = 30 . total protein = 40. greater.. hmm. it means y is somewhat more than it should be. this implies x > 100. x= 150 , then y=150 protein from x = 15 and from y = 22.5 total = 37.5..lesser so answer is between 100 and 150 . if we see there are two choices 140 and 145. which one it should be? well after increasing x by 50 we notice that we reduced total protein from 40 to 37.5 means 2.5. We just need to reduce the protein by 2.
Let us try 140 with this, protein from x = 14 , protein from y = 16+8 = 24. total = 38. this works!



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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]
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07 Aug 2016, 10:53
.10x+.15(300x)=38 x=140 grams



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A diet contains 300 grams of a mixture of two foods, food X [#permalink]
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07 Aug 2016, 13:25
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Take equal proportion to have an idea of ratio,150 each. X will give 15g, Y will give 22.5g which is closer to 38 (37.5) A little thought on the options D& E will give us E as the answer Sent from my iPhone using GMAT Club Forum mobile app



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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]
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07 Aug 2016, 21:52
I am a little confused about the wording here. The question says " a diet provides exactly 38 grams of protein daily..." is it referring to the same diet or some other diet which could be more or less than 300 grams? I feel if it is referring to the same diet then it should mention "THE diet provides...", don't you think? 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



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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]
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25 Sep 2016, 06:46
10/100 (x) + 15/100 (300x) = 38
10/100 (x) + 45  15/100 (x) = 38
5/100 (x) = 7 > 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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22 Nov 2017, 05:43
Bunuel wrote: 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 139.8hence the answer is E Keep it simple: \(0.1x+0.15(300x)=38\) > \(x=140\) (exactly). Answer: E. hi Bunuel really very simple, man



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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]
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22 Nov 2017, 08:24
Let x, y be the weight of food X, food Y in the mixture, respectively. We have: x+y = 300 and 0,1x + 015y = 38 => x = 140. Hence, the answer is E.



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Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]
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22 Nov 2017, 13:19
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 We can let x = the amount of X and y = the amount of Y. Let’s create two equations: x + y = 300 y = 300  x And 0.1x + 0.15y = 38 0.1x + 0.15(300  x) = 38 0.1x + 45  0.15x = 38 7 = 0.05x 140 = x Answer: E
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