Stephanie has a recipe that calls for StartFraction 2 over 3 EndFraction tablespoons of vanilla to make 3 and StartFraction 1 over 2 EndFraction dozen cookies.
How many tablespoons of vanilla are needed per dozen cookies?
Answer options with 4 options
A.
StartFraction 1 over 21 EndFraction
B.
StartFraction 1 over 7 EndFraction
C.
StartFraction 4 over 21 EndFraction
D.
StartFraction 3 over 7 EndFraction
To find the number of tablespoons of vanilla needed per dozen cookies, we can set up a proportion.
We can set up the proportion:
(2/3 tablespoons) / (3 + 1/2 dozen cookies) = x tablespoons / 1 dozen cookies
Multiplying both sides by (3 + 1/2 dozen cookies) yields:
(2/3 tablespoons) = x tablespoons / 1 dozen cookies * (3 + 1/2 dozen cookies)
Simplifying the right side gives:
(2/3 tablespoons) = x tablespoons / (1 + 1/6 dozen cookies)
Next, we can cross-multiply:
2/3 tablespoons * (1 + 1/6 dozen cookies) = x tablespoons
2/3 tablespoons * (7/6 dozen cookies) = x tablespoons
Multiplying the numerators and denominators gives:
(14/18) tablespoons * (7/6) = x tablespoons
Simplifying the expression gives:
(7/9) tablespoons = x tablespoons
Therefore, the number of tablespoons of vanilla needed per dozen cookies is StartFraction 7 over 9 EndFraction tablespoons.
The answer is not among the options provided.