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Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad

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Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad  [#permalink]

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New post 19 Aug 2018, 09:13
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Question Stats:

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Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

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Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad  [#permalink]

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New post 08 Dec 2018, 18:02
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Bunuel wrote:
Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

Excellent opportunity for the k technique:

\(\left\{ \matrix{
\,{\rm{oil}} = 3k\,\,\,\,\,\, \to \,\,\,\,\,\,3k \le 8\,\,\, \Rightarrow \,\,\,k \le 2{2 \over 3} \hfill \cr
\,{\rm{vin}} = 2k\,\,\,\,\,\, \to \,\,\,\,\,\,2k \le 7\,\,\, \Rightarrow \,\,\,k \le 3{1 \over 2} \hfill \cr
\,{\rm{wat}} = k \hfill \cr} \right.\)

\(?\,\,:\,\,\left( {3k + 2k + k} \right)\,\,{\rm{where}}\,\,k = 2{2 \over 3}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 6\left( {2 + {2 \over 3}} \right) = 12 + 4 = 16\)


This solution follows the notations and rationale taught in the GMATH method.

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Fabio.
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Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad  [#permalink]

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New post 19 Aug 2018, 09:56
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Bunuel wrote:
Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16



By Q-stem : \(O:V:W=3:2:1\) , so for 8 cups of oil we need = \(\frac{8}{3}*2\) =\(5 \frac{1}{3}\) \(<7\) cups of Vineger
And as \(V:W =2:1\), the amount of water required is \(\frac{8}{3}\).
Hence total salad : \(8\)+\(\frac{8}{3}*2\) + \(\frac{8}{3}\) = \(8+8 =16\) cups
Hence Ans E.
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Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad  [#permalink]

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New post 10 Dec 2018, 11:04
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Bunuel wrote:
Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16


GIVEN: oil: vinegar : water = 3 : 2 : 1

Let's first try to use ALL 8 cups of oil
Take 3 : 2 : 1 and multiply all 3 parts by 8/3 to get the EQUIVALENT ratio 8 : 16/3 : 8/3
Simplify to get: 8 : 5 1/3 : 2 2/3
So, in this case, the dressing is comprised of 8 cups of oil, 5 1/3 cups of vinegar, and 2 2/3 cups of water
Notice that we have enough vinegar to make this batch.

8 cups + 5 1/3 cups + 2 2/3 cups = 16 cups
So, the TOTAL volume = 16 cups

IMPORTANT: Notice that 16 is the biggest answer choice.
This means we need not explore what happens when we try to use ALL 7 cups on the vinegar, since the answer choices tell us that we will NOT get a value greater than 16

Answer: E

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Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad  [#permalink]

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New post 15 Mar 2019, 18:53
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Bunuel wrote:
Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16



We can create the ratio of oil : vinegar : water = 3x : 2x : x

Since Larry has 8 cups of oil, we have:

3x = 8

x = 8/3 = 2 ⅔

Since Larry has 7 cups of vinegar, we have:

2x = 7

x = 7/2 = 3.5

We see that we must use the smaller of the two values of x since, if we used 3.5 for x, we would need to have 3 x 3.5 = 10.5 cups of oil (but we have only 8 cups of oil).

Since the total number of cups of dressing is 3x + 2x + x = 6x and x = 8/3, the total number of cups of dressing that can be made is 8/3 x 6 = 16 cups.

Answer: E
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Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad   [#permalink] 15 Mar 2019, 18:53
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