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.
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.
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