Start by finding the unit rate for Elyse’s recipe. You need to find the number of cups of lemonade concentrate per 1 cup of water. What can you divide 1

Question

7
3
​
cups of water by to find 1 cup of water?
Elyse's Lemonade Recipe
÷
Water
(cups) Lemonade Concentrate
(cups)
1
7
3
​

2
1
​

1 ?

Answer 1

To find the unit rate of lemonade concentrate per 1 cup of water, you need to find the ratio of lemonade concentrate to water and then adjust it to a 1 cup of water situation.

Elyse's recipe provides:

• Water: $\frac{17}{3}$ cups
• Lemonade Concentrate: $2\frac{1}{2}$ cups, which can be written as $\frac{5}{2}$ cups (since $2\frac{1}{2}$ = $2+\frac{1}{2}=\frac{4}{2}+\frac{1}{2}=\frac{5}{2}$).

Next, to find out how many cups of lemonade concentrate correspond to 1 cup of water, we can set up the ratio:

$$\text{Lemonade Concentrate}:\text{Water}=\frac{5}{2}:\frac{17}{3}$$

Now, we want to find the concentrate per 1 cup of water:

To do this, we divide both sides of the ratio by $\frac{17}{3}$:

$$\text{Concentrate per 1 cup of water}=\frac{\frac{5}{2}}{\frac{17}{3}}=\frac{5}{2}\times \frac{3}{17}$$

Calculating this gives:

$$\frac{5\times 3}{2\times 17}=\frac{15}{34}$$

Thus, the unit rate is $\frac{15}{34}$ cups of lemonade concentrate per 1 cup of water.