Question

Elyse and Jamir each make lemonade. Elyse mixes 1
7
3
​
cups of water with
2
1
​
cups of lemonade concentrate. Jamir mixes 1
3
1
​
cups of water with
5
2
​
cups of lemonade concentrate. Which lemonade has a more lemony taste?
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
7
3
​
cups of water by to find 1 cup of water?
Elyse's Lemonade Recipe
÷
1

3
7
Water
(cups) Lemonade Concentrate
(cups)
1
7
3
​

2
1
​

1 ?
You got it!
To keep the ratio equivalent, you need to divide
2
1
​
by 1
7
3
​
also. How many cups of lemonade concentrate does Elyse’s recipe need for 1 cup of water? Solve
2
1
​
÷ 1
7
3
​
on paper, then enter your answer on Zearn.
Elyse's Lemonade Recipe
÷ 1
7
3
​

÷ 1
7
3
​

Water
(cups) Lemonade Concentrate
(cups)
1
7
3
​

2
1
​

1

Answer 1

To find out how many cups of lemonade concentrate Elyse's recipe requires for 1 cup of water, we'll first convert the mixed numbers to improper fractions and then perform the division.

Elyse's recipe uses:
- 1 7/3 cups of water
- 2 1/1 cups of lemonade concentrate

### Step 1: Convert Mixed Numbers to Improper Fractions

1. Convert 1 7/3 cups of water:
- To convert, multiply the whole number (1) by the denominator (3) and add the numerator (7).
\[
1 \times 3 + 7 = 3 + 7 = 10 \quad \text{so} \quad 1 \frac{7}{3} = \frac{10}{3}
\]

2. Convert 2 1/1 cups of lemonade concentrate:
- Since 1/1 is equal to 1, 2 1/1 becomes:
\[
2 \times 1 + 1 = 2 + 1 = 3 \quad \text{so} \quad 2 \frac{1}{1} = 3
\]

Now we have:
- Elyse's water: \( \frac{10}{3} \) cups
- Elyse's lemonade concentrate: \( 3 \) cups

### Step 2: Divide Lemonade Concentrate by Water

To find the number of cups of lemonade concentrate per 1 cup of water, we perform the following division:
\[
\text{Lemonade Concentrate} \div \text{Water} = 3 \div \frac{10}{3}
\]
To divide by a fraction, we multiply by its reciprocal:
\[
3 \div \frac{10}{3} = 3 \times \frac{3}{10} = \frac{9}{10}
\]

### Conclusion

Elyse's recipe requires \( \frac{9}{10} \) cups of lemonade concentrate for 1 cup of water.

Now, to determine which lemonade has a more lemony taste, we can repeat a similar process for Jamir's lemonade recipe and compare the two values. If you would like to proceed with Jamir's calculations, please let me know!