Question

2. Jada is making lemonade for a get-together with her friends. Sheexpects a total of 5 to 8 people to be there (including herself). She plansto prepare 2 cups of lemonade for each person. The lemonade recipe callsfor 4 scoops of lemonade powder for each quart of water. Each quart isequivalent to 4 cups. Let n represent the number of people at the get-together, c the number of cups of water, and L the number of scoops oflemonade powder. Select ALL the mathematical statements that representthe quantities and constraints in the situation. *n> 55sns 8C = 2nLECL> 1010 SLS 16

Answer 1

Let's write the first inequality, the number of people:

`5\leq n\leq8`

Now, since she plans to prepare 2 cups of water per person, we multiply 5 times 2, and 8 times 2 in the equation above; that will be the number of cups:

`10\leq c\leq16`

The next step is to find the number of required scoops. There are two ratios that tell us how many scoops of powder we need.

`\begin{gathered} \frac{4\text{ scoops}}{1\text{ quart}}\rightarrow ratio\text{ 1} \\ \frac{1\text{ quart}}{4\text{ cups}}\rightarrow ratio\text{ 2} \\ 10\text{cups}\cdot\frac{4\text{ scoops}}{1\text{ quart}}\cdot\frac{1\text{ quart}}{4\text{ cups}}\leq L\leq16\text{cups}\cdot\frac{4\text{ scoops}}{1\text{ quart}}\cdot\frac{1\text{ quart}}{4\text{ cups}} \\ 10\leq L\leq16 \end{gathered}`

After all of this, we can assure that the expressions 5<=n<=8, c=2n, L=c, 10<=L<=16

are completely true.