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A recipe for salad dressing asks for 2 1 4 2 4 1 ​ ​ cups​ of olive oil and 3 4 4 3 ​ ​ cups of vinegar. How many cups of olive oil do you need to mix with 12 12​ cups of vinegar? cups cups Preview ​ How many cups of vinegar do you need to mix with 27 8 8 27 ​ ​ cups of olive oil? cups cups Preview ​ How many cups of olive oil do you need to make 100 100​ cups of salad dressing? If needed, enter your answer as a mixed number. cups cups Preview

1 Answer

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1: You need to mix 24 1 5 ​ ​ cups of olive oil with 12 12​ cups of vinegar.

2: You need to mix 27 8 8 27 ​ ​ cups of olive oil with 96 ​ ​ cups of vinegar.

3: You need to use 62.5 ​ ​ cups of olive oil to make 100 100​ cups of salad dressing.

Question 1:

How many cups of olive oil do you need to mix with 12 12​ cups of vinegar?

To answer this question, we can set up a proportion. Let x be the number of cups of olive oil we need. We have the following proportion:

x / 2 1 4 2 4 1 ​ ​ = 12 12​ / 3 4 4 3 ​ ​

Simplifying the fractions, we get:

x / 18 5 ​ ​ = 12 12​ / 16 9 ​ ​

Multiplying both sides by the cross product, we get:

x = (18 5 ​ ​) * (12 12​ / 16 9 ​ ​)

Calculating, we get:

x = 24 1 5 ​ ​ cups of olive oil

Therefore, you need to mix 24 1 5 ​ ​ cups of olive oil with 12 12​ cups of vinegar.

Question 2:

How many cups of vinegar do you need to mix with 27 8 8 27 ​ ​ cups of olive oil?

Using the same approach as in question 1, we can set up a proportion:

3 4 4 3 ​ ​ / x = 27 8 8 27 ​ ​ / 2 1 4 2 4 1 ​ ​

Simplifying the fractions, we get:

16 9 ​ ​ / x = 27 8 8 27 ​ ​ / 18 5 ​ ​

Multiplying both sides by the cross product, we get:

x = (16 9 ​ ​) * (27 8 8 27 ​ ​ / 18 5 ​ ​)

Calculating, we get:

x = 96 ​ ​ cups of vinegar

Therefore, you need to mix 27 8 8 27 ​ ​ cups of olive oil with 96 ​ ​ cups of vinegar.

Question 3:

How many cups of olive oil do you need to make 100 100​ cups of salad dressing?

Let's assume that we have x cups of olive oil and y cups of vinegar. We know that the total volume of the salad dressing is 100 cups, so we can set up the equation:

x + y = 100

We also know that the ratio of olive oil to vinegar is 2:3. This means that we can express y in terms of x:

y = (3/5)x

Substituting this expression into the first equation, we get:

x + (3/5)x = 100

Combining like terms, we get:

(8/5)x = 100

Dividing both sides by 8/5, we get:

x = 62.5 ​ ​ cups of olive oil

Therefore, you need to use 62.5 ​ ​ cups of olive oil to make 100 100​ cups of salad dressing.

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