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Miguel is mixing up a salad dressing. Regardless of the numb

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Re: Miguel is mixing up a salad dressing. [#permalink]

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New post 26 Jul 2010, 10:05
The wording of this really confused me. It seems like you could either double the proportion of vinegar or the actual amount and get completely different answers. I wasted a lot of time assuming it was the proportion he got wrong - I thought he went from 1/4 vinegar to 1/2 vinegar.

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Re: Miguel is mixing up a salad dressing. Regardless of the number of serv [#permalink]

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New post 03 May 2011, 23:29
let the total quantity be a multiple of 8 and 4 = 64
thus original quantities are 40, 16 and 2.6 each for sugar,salt and pepper.
new quantities are 40,32,0,2.6 and 2.6 where sugar = 0

thus new total is 77.2

thus % = 40/77.2 < 1/2
closest approximation is 15/29 < 1/2 Hence A.
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Re: Miguel is mixing up a salad dressing. Regardless of the number of serv [#permalink]

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New post 04 May 2011, 10:53
Let x be the original mix.

New mix is as follows

5x/8 - olive
2x/4 - vinegar
x/24 - Sugar
x/24 - pepper

=29x/24

Pepper proportion of new mix = (5/8)*(24/29) = 15/29

Answer is A

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Re: Miguel is mixing up a salad dressing. [#permalink]

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New post 23 Jul 2011, 05:30
Hi,

nonameee wrote:
AndreG wrote:
Quote:

That's not what I've asked. I understand where you got the numbers and 24 is very clear to me.

I just thought that since he changed the ratio of various ingredients, the ratio of oil will be different as well. So I don't understand why we can assume that the ratio of the oil should remain the same? It if remains the same (as in your calculations, i.e., oil = 15x) the weight of the mixture will change. In my calculations I assumed that the weight of the mixture stays the same and the rate of the oil changes.

Maybe I didn't understand the the question well.


Yes I had the same problem!

I filled the mixture with 1/2 vinegar (i.e. 12), 1 salt and 1 pepper --> ending up with 10 left for oil, hence 10/24 = 5/12 is the proportion of oil in the dressing.

Someone please clarify where we went wrong... :(


Yeah, I had the same reasoning.



Though I understood the correct reasoning, I am still not clear on what is wrong in these ones.

Can someone please clarify..

Thanks

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Re: Miguel is mixing up a salad dressing. [#permalink]

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New post 15 Sep 2011, 01:48
take 24 as the total mixture.

O:V:Slt:P:Su
15:6:1:1:1 .... planned ratio

O:V:Slt:P
15:12:1:1 .... actual ratio

O = 15/29
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Re: Miguel is mixing up a salad dressing. [#permalink]

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New post 18 Dec 2011, 03:38
AndreG wrote:
Quote:

That's not what I've asked. I understand where you got the numbers and 24 is very clear to me.

I just thought that since he changed the ratio of various ingredients, the ratio of oil will be different as well. So I don't understand why we can assume that the ratio of the oil should remain the same? It if remains the same (as in your calculations, i.e., oil = 15x) the weight of the mixture will change. In my calculations I assumed that the weight of the mixture stays the same and the rate of the oil changes.

Maybe I didn't understand the the question well.


Yes I had the same problem!

I filled the mixture with 1/2 vinegar (i.e. 12), 1 salt and 1 pepper --> ending up with 10 left for oil, hence 10/24 = 5/12 is the proportion of oil in the dressing.

Someone please clarify where we went wrong... :(



Exactly!!!!!

I mean, I completely understand the answer - 15/29. I too would'v chosen 24 or a similar number as an LCM.But, what's wrong here... It jus happened that I got this approach..
Stuck here.. Can some one explain.. Experts....???

Thanks!

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Re: Miguel is mixing up a salad dressing. [#permalink]

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New post 29 Dec 2013, 11:25
The problem with folks who are getting 5/12 as the answer, the point you folks are messing up is that you are trying to balance the missing components (by adding) to Olive oil. (I will explain this while calculating blotched mix)

I am just using the fractions given in the question, and not taking any LCM as suggested in few posts (to avoid confusion)

Original mix.

Olive oil = 5/8
Vinegar = 1/4
Remaining = 1 -(5/8+1/4) = 1/8
Even mixture of salt, pepper and sugar = (1/8)/3 = 1/24 each.

Blotched mix.

Olive oil = 5/8
Vinegar = 2 * 1/4 = 1/2
Remaining = 1/24 + 1/24

Folks are working this out as 1 - ( vinegar + remaining) = 1 - (1/2 + 1/24 + 1/24) = 1 - (7/12) = 5/12 (and hence this is understood as the proportion of Olive oil)
The mistake is that, Olive oil's proportion is not changed and is calculated as below.


Proportion of olive oil in blotched mix = Olive oil / sum of components in blotched mix.
= (5/8) / ( 5/8 + 1/2 + 1/24 + 1/24)
= (5/8) / ( 15/24 + 12/24 + 1/24 + 1/24)
= (5/8) / ( 29/24)
= 5/8 x 24/29
= 15/29 (ans)
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Re: Miguel is mixing up a salad dressing. Regardless of the numb [#permalink]

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New post 29 Dec 2013, 11:34
Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
A) 15/29
B) 5/8
C) 5/16
D) 1/2
E) 13/27

Olive oil = 5/8 = 15/24 --> 15 parts out of 24;
Vinegar = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;

If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are olive oil --> proportion = 15/29.

Answer: A.

P.S. Took 24 as common denominator so that share of each ingredient to be integer.

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Re: Miguel is mixing up a salad dressing. Regardless of the numb [#permalink]

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New post 18 Apr 2014, 14:17
OO: 5/8
V: 2/8

S/S/P each 1/24

After conditions applied:

OO: 5/8
V: 4/8

S/S/P = 1/24 + 1/24

5/8/{4/8 + 1/24 + 1/24 + 5/8}

15/29
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Re: Miguel is mixing up a salad dressing. Regardless of the number of serv [#permalink]

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New post 10 Oct 2014, 08:29
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Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
A) 15/29
B) 5/8
C) 5/16
D) 1/2
E) 13/27

Olive oil = 5/8 = 15/24 --> 15 parts out of 24;
Vinegar = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;

If vinegar = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are olive oil --> proportion = 15/29.

Answer: A.

P.S. Took 24 as common denominator so that share of each ingredient to be integer.

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OPEN DISCUSSION OF THIS QUESTION IS HERE: miguel-is-mixing-up-a-salad-dressing-regardless-of-the-109740.html
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Miguel is mixing up a salad dressing. Regardless of the number of serv [#permalink]

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New post 16 Oct 2014, 01:02
Olive ................. Vinegar .............................. Salt .......... Sugar ............ Pepper ................ Total

\(\frac{5}{8}\) ........................ \(\frac{2}{8}\) ................................ \(\frac{1}{24}\) ......... \(\frac{1}{24}\) ................ \(\frac{1}{24}\) ..................... 1

Vinegar doubled; sugar forgot

\(\frac{5}{8}\) ......................... \(\frac{2}{8} * 2\) ........................ """"" .............. 0 .................. """" ....................... \(1 + \frac{1}{4} - \frac{1}{24} = \frac{29}{24}\)

Proportion required\(= \frac{\frac{5}{8}}{\frac{29}{24}} = \frac{15}{29}\)

Answer = A
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Re: Miguel is mixing up a salad dressing. Regardless of the number of serv   [#permalink] 16 Oct 2014, 01:02

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