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 A and Batch C have the same number of cups of chocolate chips per cookie.
Batch A and Batch B have the same number of cups of chocolate chips per cookie.
Batch C uses less cups of chocolate chips per dozen than Batch A.
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 would use 6 cups of chocolate chips to make 12 dozen cookies.
Calculate each unit rate and then select the true statements below.
Batch A and Batch C have the same number of cups of chocolate chips per cookie.
Batch A and Batch B have the same number of cups of chocolate chips per cookie.
Batch C uses less cups of chocolate chips per dozen than Batch A.
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 would use 6 cups of chocolate chips to make 12 dozen cookies.
Answers
GPT 3.5
To calculate the unit rate, we divide the number of cups of chocolate chips by the number of cookies.
For Batch A:
Cups of chocolate chips / Number of cookies = 2 cups / 48 cookies = 0.042 cups per cookie
For Batch B:
Cups of chocolate chips / Number of cookies = 3 cups / 36 cookies = 0.083 cups per cookie
For Batch C:
Cups of chocolate chips / Number of cookies = 1.5 cups / 36 cookies = 0.042 cups per cookie
Now, let's analyze each statement:
Batch A and Batch C have the same number of cups of chocolate chips per cookie. - This statement is TRUE, as both batches have a unit rate of 0.042 cups per cookie.
Batch A and Batch B have the same number of cups of chocolate chips per cookie. - This statement is FALSE, as Batch A has a unit rate of 0.042 cups per cookie and Batch B has a unit rate of 0.083 cups per cookie.
Batch C uses less cups of chocolate chips per dozen than Batch A. - This statement is TRUE, as Batch A uses 2 cups for 48 cookies, while Batch C uses 1.5 cups for 36 cookies. Therefore, Batch C uses fewer cups of chocolate chips per dozen.
Batch B uses 1 cup of chocolate chips per 1 dozen cookies. - This statement is FALSE, as Batch B uses 3 cups for 36 cookies, which is not equivalent to 1 cup per dozen.
Batch B uses less cups of chocolate chips per dozen than Batch C. - This statement is TRUE, as Batch B uses 3 cups for 36 cookies while Batch C uses 1.5 cups for 36 cookies. Therefore, Batch B uses fewer cups of chocolate chips per dozen.
Batch C would use 6 cups of chocolate chips to make 12 dozen cookies. - This statement is TRUE, as Batch C uses 1.5 cups for 36 cookies. To make 12 dozen cookies (144 cookies), Batch C would require (1.5 cups / 36 cookies) x 144 cookies = 6 cups of chocolate chips.
Overall, the true statements are:
- Batch A and Batch C have the same number of cups of chocolate chips per cookie.
- Batch C uses less cups of chocolate chips per dozen than Batch A.
- Batch B uses less cups of chocolate chips per dozen than Batch C.
- Batch C would use 6 cups of chocolate chips to make 12 dozen cookies.
For Batch A:
Cups of chocolate chips / Number of cookies = 2 cups / 48 cookies = 0.042 cups per cookie
For Batch B:
Cups of chocolate chips / Number of cookies = 3 cups / 36 cookies = 0.083 cups per cookie
For Batch C:
Cups of chocolate chips / Number of cookies = 1.5 cups / 36 cookies = 0.042 cups per cookie
Now, let's analyze each statement:
Batch A and Batch C have the same number of cups of chocolate chips per cookie. - This statement is TRUE, as both batches have a unit rate of 0.042 cups per cookie.
Batch A and Batch B have the same number of cups of chocolate chips per cookie. - This statement is FALSE, as Batch A has a unit rate of 0.042 cups per cookie and Batch B has a unit rate of 0.083 cups per cookie.
Batch C uses less cups of chocolate chips per dozen than Batch A. - This statement is TRUE, as Batch A uses 2 cups for 48 cookies, while Batch C uses 1.5 cups for 36 cookies. Therefore, Batch C uses fewer cups of chocolate chips per dozen.
Batch B uses 1 cup of chocolate chips per 1 dozen cookies. - This statement is FALSE, as Batch B uses 3 cups for 36 cookies, which is not equivalent to 1 cup per dozen.
Batch B uses less cups of chocolate chips per dozen than Batch C. - This statement is TRUE, as Batch B uses 3 cups for 36 cookies while Batch C uses 1.5 cups for 36 cookies. Therefore, Batch B uses fewer cups of chocolate chips per dozen.
Batch C would use 6 cups of chocolate chips to make 12 dozen cookies. - This statement is TRUE, as Batch C uses 1.5 cups for 36 cookies. To make 12 dozen cookies (144 cookies), Batch C would require (1.5 cups / 36 cookies) x 144 cookies = 6 cups of chocolate chips.
Overall, the true statements are:
- Batch A and Batch C have the same number of cups of chocolate chips per cookie.
- Batch C uses less cups of chocolate chips per dozen than Batch A.
- Batch B uses less cups of chocolate chips per dozen than Batch C.
- Batch C would use 6 cups of chocolate chips to make 12 dozen cookies.