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.