Final answer:
To find the amount of vanilla needed per dozen cookies, divide the amount needed for 42 cookies by 42 and then multiply by 12. The answer is 1/3 tablespoon of vanilla.
Step-by-step explanation:
To find out how many tablespoons of vanilla are needed per dozen cookies, we need to first determine the amount of vanilla needed for the given number of cookies. The recipe calls for two-thirds tablespoon of vanilla for three and a half dozen cookies.
To find the amount of vanilla needed for a single dozen cookies, we can set up a proportion. Three and a half dozen cookies is equivalent to 3.5 x 12 = 42 cookies. So, two-thirds tablespoon of vanilla is needed for 42 cookies.
Now, to find how many tablespoons of vanilla are needed for a single dozen cookies, we divide the amount needed for 42 cookies by 42 and then multiply by 12.
Let's calculate that:
Amount needed for 42 cookies = (2/3) tablespoon
Amount needed for 1 cookie = (2/3) / 42 tablespoon
Amount needed for 1 dozen cookies = ((2/3) / 42) x 12 tablespoon
To simplify the calculation, we can write the fractions in terms of tablespoons.
2/3 tablespoon = 4/6 tablespoon = 2/6 tablespoon = 1/3 tablespoon
So, 1/3 tablespoon of vanilla is needed per dozen cookies.