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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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Math Expert
Joined: 02 Sep 2009
Posts: 51071
Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad  [#permalink]

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19 Aug 2018, 08:13
00:00

Difficulty:

85% (hard)

Question Stats:

41% (01:20) correct 59% (02:10) wrong based on 51 sessions

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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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19 Aug 2018, 08:56
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1
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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Please let me know if I am going in wrong direction.
Thanks in appreciation.

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 534
Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad  [#permalink]

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08 Dec 2018, 17:02
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.

Regards,
Fabio.
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Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad &nbs [#permalink] 08 Dec 2018, 17:02
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