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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, 10:49

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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?

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

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30 Jul 2012, 06:52

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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Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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).

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

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13 Oct 2013, 12:33

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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, 21:12

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, 06:53

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]

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06 Aug 2016, 23:18

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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07 Aug 2016, 05:02

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!

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

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07 Aug 2016, 12:25

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

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

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07 Aug 2016, 20:52

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?

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