Jada is making lemonade for a get-together with 5 to 8 people. She plans to prepare 2 cups of lemonade for each person. The recipe requires 4 scoops of lemonade powder for each quart of water, and each quart is equivalent to 4 cups. We are given that $n$ represents the number of people, $c$ represents the number of cups of water, and $l$ represents the number of scoops of lemonade powder. We need to select all mathematical statements that represent the quantities and constraints in the situation.

1. Problem Description

Jada is making lemonade for a get-together with 5 to 8 people. She plans to prepare 2 cups of lemonade for each person. The recipe requires 4 scoops of lemonade powder for each quart of water, and each quart is equivalent to 4 cups. We are given that $n$ represents the number of people, $c$ represents the number of cups of water, and $l$ represents the number of scoops of lemonade powder. We need to select all mathematical statements that represent the quantities and constraints in the situation.

2. Solution Steps

A. $5 < n < 8$: This is incorrect because the number of people can be 5 or

8. The inequality should include 5 and

8. B. $5 \le n \le 8$: This is correct. The number of people is between 5 and 8, inclusive.

C. $c = 2n$: This is correct. She plans to prepare 2 cups of lemonade for each person. Therefore, the total number of cups $c$ is equal to 2 times the number of people $n$.

D. $l = c$: This is incorrect. Since 4 scoops of lemonade powder are required for 4 cups of water (1 quart), the number of scoops should be equal to the number of cups, but this is only in the case when we are using the exact recipe. The problem does not state whether she is using the exact recipe or if the quart is the measurement for a batch. The question only says that the recipe calls for 4 scoops for each quart. Since it also says that each quart is equal to 4 cups, then, when using the exact recipe, the number of scoops and the number of cups will be equal. However, let's find $l$ as a function of $c$ with the other given information.

Since 4 scoops of powder is needed for every 4 cups of water, we can say that for $c$ cups of water, we need $l = c$ scoops of lemonade powder. The problem states each quart is equivalent to 4 cups. Since a quart requires 4 scoops, the number of scoops $l$ would equal the number of cups $c$, but this is only using the EXACT recipe.

E. $10 < c < 16$: This is incorrect.

The number of cups $c = 2n$. Since $5 \le n \le 8$, then $2(5) \le 2n \le 2(8)$, which means $10 \le c \le 16$. This should include 10 and

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6. F. $10 \le l \le 16$:

Since $l = c$, and $10 \le c \le 16$, then we also have $10 \le l \le 16$. This is correct.

Alternatively, the number of scoops required is equal to the number of cups. Since the number of cups ranges from $2*5=10$ to $2*8=16$, then the number of scoops also ranges from 10 to 16, inclusive.

3. Final Answer

B. $5 \le n \le 8$

C. $c = 2n$

F. $10 \le l \le 16$