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

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Intern
Joined: 07 May 2003
Posts: 8
Location: Dallas
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
[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.
Manager
Joined: 12 Mar 2003
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20 May 2003, 21:08
1
KUDOS
1.... 10/100*X + 15/100*Y = 38 (protein)

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

Solve for X = 140
Manager
Status: I will not stop until i realise my goal which is my dream too
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Posts: 218
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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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Expert's post
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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

hence the answer is E

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

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Manager
Joined: 25 Jun 2012
Posts: 66
Location: India
WE: General Management (Energy and Utilities)
Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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13 Aug 2012, 00:41
1
KUDOS
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
Director
Joined: 03 Aug 2012
Posts: 882
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
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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
1
KUDOS
X+Y = 300

0.1X + 0.15Y = 38

X=140
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Manager
Joined: 17 Aug 2015
Posts: 105
Re: A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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07 Aug 2016, 06:02
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!
Director
Joined: 07 Dec 2014
Posts: 927
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(300-x)=38
x=140 grams
Manager
Joined: 20 Mar 2015
Posts: 72
Location: United States
Concentration: General Management, Strategy
WE: Design (Manufacturing)
A diet contains 300 grams of a mixture of two foods, food X [#permalink]

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07 Aug 2016, 13:25
1
KUDOS
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
Manager
Joined: 28 Apr 2016
Posts: 100
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
Current Student
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Posts: 405
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 (300-x) = 38

10/100 (x) + 45 - 15/100 (x) = 38

-5/100 (x) = -7 --> x= 140
Senior Manager
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Posts: 277
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 139.8

hence the answer is E

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

hi Bunuel
really very simple, man
Intern
Joined: 12 Oct 2017
Posts: 39
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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Posts: 2127
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

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Re: A diet contains 300 grams of a mixture of two foods, food X   [#permalink] 22 Nov 2017, 13:19
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