Question

you’re making desert, but your snickerdoodle cookie recipe needs adjustment. your snickerdoodle cookie recipe makes 3 dozen cookies, but you need 4 dozen cookies. if the recipe requires 1 and 3/4 cups of vegetable oil, 2 and 1/4 teaspoons of almond extract, 2 and 1/2 teaspoons of cinnamon, how much of the these ingredients are necessary for 4 dozen cookies? simplify your answer.

Answer 1

Proportions

All of the ingredients are given in amounts enough to make 3 dozen cookies. But we want to know how much of them are required to make 4 dozen cookies.

Following the proportions rules, if we want 4 and have 3, the adjustment must be 4 / 3, or four thirds.

For example, if you use 6 eggs for 3 dozen cookies, you now need 6*4/3=8 eggs.

This proportion will be applied to all of the ingredients as follows.

We needed 1 and 3/4 cups of vegetable oil. Expressing that as a single fraction:

`1+(3)/(4)=(7)/(4)`

The new amount of vegetable oil will be:

`(4)/(3)\cdot(7)/(4)=(7)/(3)=(6+1)/(3)=2(1)/(3)`

We now need 2 and 1/3 cups of vegetable oil.

It's required to use 2 and 1/4 teaspoons of almond extract. Expressing as a single fraction:

`2+(1)/(4)=(9)/(4)`

The new amount of almond extract is:

`(4)/(3)\cdot(9)/(4)=3`

Now we need exactly 3 teaspoons of almond extract.

Finally, the recipe required 2 and 1/2 teaspoons of cinnamon. The equivalent fraction is:

`2+(1)/(2)=(5)/(2)`

This means the new amount of cinnamon is:

`(4)/(3)\cdot(5)/(2)=(10)/(3)=(9+1)/(3)=3(1)/(3)`

We now need 3 and 1/3 teaspoons of cinnamon.

Summarizing, for 4 dozen cookies we need:

2 and 1/3 cups of vegetable oil

3 teaspoons of almond extract

3 and 1/3 teaspoons of cinnamon