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

BTGmoderatorDC 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

OA E

Source: Manhattan Prep

Given that there is no constraint with the usage of water, we must focus on oil and vinegar.

The ratio of oil and vinegar is 3 : 2.

Let's interpret above.

Taking the ratio of oil and vinegar is 3 : 2 as 1 : 2/3

• For 1 cup of oil, we need 2/3 cups of vinegar => For 8 cup of oil, we need 8*(2/3) = 16/3 cups of vinegar, which is less than 7. The number of cups of water needed = 8*(1/3) = 8/3. So, this can work.

Number of cups possible = 8 + 16/3 + 8/3 = 16 cups

Taking the ratio of oil and vinegar is 3 : 2 as 3/2 : 1

• For 1 cup of vinegar, we need 3/2 cups of oil => For 7 cup of vinegar, we need 7*(3/2) = 21/2 cups of oil, which is more than 8 cups, so this is not possible.

Thus, the maximum number of cups of salad dressing = 16 cups

The correct answer: E

Hope this helps!

-Jay
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BTGmoderatorDC 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

OA E

Source: Manhattan Prep

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

Cheers,
Brent

BTGmoderatorDC 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

OA E

Source: Manhattan Prep

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