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.
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.
To solve this problem, we need to calculate the unit rate for each batch of cookies.
1. Batch A: Requires 2 cups of chocolate chips for 4 dozen cookies.
Unit rate: 2 cups / 4 dozen = 0.5 cups per dozen cookies
2. Batch B: Requires 3 cups of chocolate chips for 3 dozen cookies.
Unit rate: 3 cups / 3 dozen = 1 cup per dozen cookies
3. Batch C: Requires 1.5 cups of chocolate chips for 3 dozen cookies.
Unit rate: 1.5 cups / 3 dozen = 0.5 cups per dozen cookies
Now let's evaluate each statement:
1. Batch A and Batch C have the same number of cups of chocolate chips per cookie. FALSE. Batch A has 0.5 cups, while Batch C has 0.5 cups per dozen cookies, not per cookie.
2. Batch A and Batch B have the same number of cups of chocolate chips per cookie. FALSE. Batch A has 0.5 cups per dozen cookies, while Batch B has 1 cup per dozen cookies.
3. Batch C uses fewer cups of chocolate chips per dozen than Batch A. TRUE. Batch A uses 0.5 cups, while Batch C only uses 0.5 cups per dozen cookies.
4. Batch B uses 1 cup of chocolate chips per 1 dozen cookies. TRUE. Batch B uses 1 cup per dozen cookies.
5. Batch B uses fewer cups of chocolate chips per dozen than Batch C. FALSE. Batch B uses 1 cup, while Batch C uses 0.5 cups per dozen cookies.
6. Batch C would use 6 cups of chocolate chips to make 12 dozen cookies. FALSE. Batch C uses 0.5 cups per dozen cookies, so for 12 dozen cookies, it would require 0.5 * 12 = 6 cups of chocolate chips.
Therefore, the true statements are:
- 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.
To calculate the unit rate for each batch, we need to determine the number of cups per cookie.
For Batch A:
- 4 dozen cookies require 2 cups of chocolate chips
- Therefore, 1 dozen cookies would require 2/4 = 0.5 cups of chocolate chips
- The unit rate for Batch A is 0.5 cups of chocolate chips per dozen cookies.
For Batch B:
- 3 dozen cookies require 3 cups of chocolate chips
- Therefore, 1 dozen cookies would require 3/3 = 1 cup of chocolate chips
- The unit rate for Batch B is 1 cup of chocolate chips per dozen cookies.
For Batch C:
- 3 dozen cookies require 1.5 cups of chocolate chips
- Therefore, 1 dozen cookies would require 1.5/3 = 0.5 cups of chocolate chips
- The unit rate for Batch C is 0.5 cups of chocolate chips per dozen cookies.
Now, let's evaluate the given statements:
1. Batch A and Batch C have the same number of cups of chocolate chips per cookie.
- True. Both Batch A and Batch C have a unit rate of 0.5 cups of chocolate chips per dozen cookies.
2. Batch A and Batch B have the same number of cups of chocolate chips per cookie.
- False. Batch A has a unit rate of 0.5 cups per dozen cookies, while Batch B has a unit rate of 1 cup per dozen cookies.
3. Batch C uses fewer cups of chocolate chips per dozen than Batch A.
- False. Both Batch A and Batch C have a unit rate of 0.5 cups per dozen cookies.
4. Batch B uses 1 cup of chocolate chips per 1 dozen cookies.
- True. The unit rate for Batch B is 1 cup per dozen cookies.
5. Batch B uses fewer cups of chocolate chips per dozen than Batch C.
- False. Batch B has a unit rate of 1 cup per dozen cookies, while Batch C has a unit rate of 0.5 cups per dozen cookies.
6. Batch C would use 6 cups of chocolate chips to make 12 dozen cookies.
- True. If 1 dozen cookies require 0.5 cups of chocolate chips, then 12 dozen cookies would require 0.5 * 12 = 6 cups of chocolate chips.
Based on the calculations, the correct statements are:
1. Batch A and Batch C have the same number of cups of chocolate chips per cookie.
4. Batch B uses 1 cup of chocolate chips per 1 dozen cookies.
6. Batch C would use 6 cups of chocolate chips to make 12 dozen cookies.