Question

Shannon has three different recipes for chocolate chip cookies. If she wants to make 4 dozen cookies from Batch A, she needs to use 2 cups of chocolate chips. If she wants to make 3 dozen cookies from Batch B, she needs to use 3 cups of chocolate chips. If she wants to make 3 dozen cookies from Batch C, she needs to use 1.5 cups of chocolate chips.

Calculate each unit rate and then select the true statements below.

Batch B uses 1 cup of chocolate chips per 1 dozen cookies.
Batch B uses less cups of chocolate chips per dozen than Batch C.
Batch C uses less cups of chocolate chips per dozen than Batch A.
Batch A and Batch B have the same number of cups of chocolate chips per cookie.
Batch A and Batch C have the same number of cups of chocolate chips per cookie.
Batch C would use 6 cups of chocolate chips to make 12 dozen cookies.

Answer 1

Compute unit rates:

- Batch A: 2 cups / 4 dozen = 0.5 cup per dozen. Per cookie: 2 cups / 48 cookies = 1/24 cup per cookie.
- Batch B: 3 cups / 3 dozen = 1 cup per dozen. Per cookie: 3 cups / 36 cookies = 1/12 cup per cookie.
- Batch C: 1.5 cups / 3 dozen = 0.5 cup per dozen. Per cookie: 1.5 cups / 36 cookies = 1/24 cup per cookie.

True/false for each statement:
- Batch B uses 1 cup of chocolate chips per 1 dozen cookies. — True
- Batch B uses less cups of chocolate chips per dozen than Batch C. — False
- Batch C uses less cups of chocolate chips per dozen than Batch A. — False (they're equal)
- Batch A and Batch B have the same number of cups of chocolate chips per cookie. — False
- Batch A and Batch C have the same number of cups of chocolate chips per cookie. — True
- Batch C would use 6 cups of chocolate chips to make 12 dozen cookies. — True

So the true statements are: 1, 5, and 6.