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

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Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to [#permalink] New post 17 Aug 2018, 18:39
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83% (01:17) correct 16% (00:34) wrong based on 12 sessions
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
[Reveal] Spoiler: OA

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Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to [#permalink] New post 25 Feb 2019, 08:09
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sandy 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 [#permalink] New post 10 Mar 2019, 11:08
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Here's how I solved it: Oil is our limiting factor. We'll have plenty of vinegar and water.

If we have 8 cups of oil and we need 3 cups to make one serving of dressing, then we can make \(\frac{8}{3}\) servings of dressing total.

Each serving of dressing is 3 + 2 + 1 = 6 cups.

So if we can make \(\frac{8}{3}\) servings of dressing, and each serving is 6 cups, then we can make \(\frac{8}{3}*6 = \frac{48}{3}= 16\) cups of dressing.
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Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to [#permalink] New post 07 Aug 2019, 18:33
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I did it this way.
Oil is our limiting factor.

From the ratio, 3 cups of oil consumes 3 cups of other ingredients (2 cups vinegar+1cup water). So, 8 cups oil should consume 8 cups of other ingredients in total.

So, total no. of final cups equals 16 cups
Re: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to   [#permalink] 07 Aug 2019, 18:33
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