Final answer:
To find out how many cups of olive oil are needed for 15 cups of vinegar, set up a proportion with the original recipe and solve for the unknown quantity. The calculation shows that you will need 40 cups of olive oil.
Step-by-step explanation:
The question requires setting up a proportion to determine how many cups of olive oil are needed when mixing with 15 cups of vinegar, given that the original recipe calls for 1½ cups of olive oil and ¾ cup of vinegar. To solve this, we can write the proportion as:
1½ cups olive oil / ¾ cup vinegar = x cups olive oil / 15 cups vinegar.
By cross-multiplying and solving for x, we get:
¾ * x = 1½ * 15
x = (1½ * 15) / ¾
x = (3/2 * 15) / (3/4)
x = 30 / ¾
x = 30 * (4/3)
x = 40
Therefore, you will need 40 cups of olive oil to mix with 15 cups of vinegar.