Question

Ingredients for 16 brownies:

2/3 cup butter, 5 ounces unsweetened chocolate, 1 and 1/2 cups sugar, 2 teaspoons vanilla, 2 eggs, 1 cup

How much of each ingredient is needed to make 12 brownies?

Answer 1

1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, 3/2 eggs, and 3/4 cups flour.

Explanation:

There are several ways to solve this, I like using proportions.

(You could also find 3/4 of every ingredient since 12 is 3/4s of 16)

We can do this by temporarily naming the amount of each ingredient a variable, and then using the proportion to find the variable.

Note that in a given proportion such as:

a/b=c/d

will always equal

a*d=b*c

This is known as cross multiplying.

For each ingredient I'm going to set up the following proportion:

`(amount of given ingredient in 16 brownies)/(16 (number of brownies)) = (variable (amount of given ingredient in 12 brownies)/(12 (new number of brownies))`

Now we can start setting up proportions for every ingredient.

Butter:

(2/3)/16=b/12

(2/3)(12)=16b

8=16b

b=1/2

Chocolate:

5/16=c/12

60=16c

c=60/16

c=15/4

Sugar:

(3/2)/16=s/12

(3/2)(12)=16s

18=16s

s=18/16

s=9/8

Vanilla:

2/16=v/12

24=16v

v=24/16

v=3/2

Eggs:

2/16=e/12

24=16e

e=3/2

Flour:

1/16=f/12

12=16f

f=3/4

Therefore, the ingredients for 12 brownies would be:

1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, 3/2 eggs, and 3/4 cups flour.