Question

stephanie has a recipe that calls for 2/3 tablespoons of vanilla to make 3 1/2 dozen cookies how many tablespoons of vanilla are needed per dozen cookies

Answer 1

Answer:

4 / 21 spoonful of vanilla

Step-by-step explanation:

3 1/2 dozens = 42 cookies

Let x = spoonful of vanilla for 1 dozen of cookies

2/3 : 42 cookies

x : 12 cookies

2/3 ÷ 42 = x ÷ 12

2/3 × 1/42 = x / 12

2 / 126 = x / 12

Cross product

2*12 = 126*x

24 = 126x

Divide both sides by 126

x = 24 / 126

= 4 / 21

x = 4 / 21 spoonful of vanilla

Per dozen of cookies requires 4/21 spoonful of vanilla

Check:

4/21 per dozen × 3 1/2 dozens

4/21 × 7/2

28 / 42

2/3 spoonful for 3 1/2 dozens

Answer 2

The total amount of dozen cookies = $3\dfrac{1}{2}$

Stephanie requires $\dfrac{2}{3} \ tablespoons$ to make $\mathsf{3\dfrac{1}{2}\ dozen \ cookies}$

Let assume that:

• (x) represents the amount of the tablespoons Stephaine needs to prepare 1 dozen cookies:

Then; we can equate both equations together as follows:

$\dfrac{2}{3} \ tablespoons$ =  $\mathsf{3\dfrac{1}{2}\ dozen \ cookies}$

x tablespoon = 1 dozen cookies

By cross multiply and making (x) the subject of the formula, we have:

$\mathbf{x \times 3\dfrac{1}{2} dozen \ cookies = \dfrac{2}{3} \ tablespoons \times 1 \ dozen \ cookies}$

$\mathbf{x =\dfrac{ \dfrac{2}{3} \ tablespoons \times 1 \ dozen \ cookies}{3\dfrac{1}{2} dozen \ cookies}}$

$\mathbf{x =\dfrac{ \dfrac{2}{3} \ tablespoons}{3\dfrac{1}{2} }}$

$\mathbf{x =\dfrac{ \dfrac{2}{3} \ tablespoons}{\dfrac{7}{2} }}$

$\mathbf{x = \dfrac{2}{3} \ tablespoons} \div {\dfrac{7}{2} }$

$\mathbf{x = \dfrac{2}{3} \ tablespoons} \times {\dfrac{2}{7} }$

$\mathbf{x = \dfrac{4}{21} \ tablespoons}}$

Therefore, the amount of tablespoons Stephaine will need to prepare a dozen cookies is: $\mathbf{ = \dfrac{4}{21} \ tablespoons}}$

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