Elyse and Jamir each make lemonade. Elyse mixes 1

To find the unit rate for Elyse's lemonade recipe, we need to determine the amount of lemonade concentrate per 1 cup of water.

Elyse's Recipe:

• Water: \(1 \frac{7}{3}\) cups
• Lemonade Concentrate: \(2 \frac{1}{2}\) cups

First, we convert the mixed numbers into improper fractions:

1. Convert \(1 \frac{7}{3}\) (water): \[ 1 \frac{7}{3} = \frac{3 \times 1 + 7}{3} = \frac{3 + 7}{3} = \frac{10}{3} \]

2. Convert \(2 \frac{1}{2}\) (lemonade concentrate): \[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]

Now, we need to divide the amount of lemonade concentrate by the amount of water to find out how much concentrate is needed for 1 cup of water:

\[ \text{Lemonade Concentrate per 1 cup of Water} = \frac{5/2}{10/3} \]

To divide by a fraction, we multiply by its reciprocal:

\[ \frac{5}{2} \times \frac{3}{10} = \frac{5 \times 3}{2 \times 10} = \frac{15}{20} = \frac{3}{4} \]

So, Elyse's recipe requires \(\frac{3}{4}\) cups of lemonade concentrate for 1 cup of water.

Now let's check Jamir's recipe to see how it compares.

Jamir's Recipe:

• Water: \(1 \frac{3}{1}\) (which is simply 3 cups)
• Lemonade Concentrate: \(5 \frac{2}{1}\) (which is simply 5 cups)

Now, we will again convert this to improper fractions:

1. Convert \(3\) to an improper fraction (it is already a whole number): \[ 3 = \frac{3}{1} \]

2. Convert \(5\) to an improper fraction (it is already a whole number): \[ 5 = \frac{5}{1} \]

Now we will find the concentrate per 1 cup of water for Jamir's recipe:

\[ \text{Lemonade Concentrate per 1 cup of Water} = \frac{5/1}{3/1} = \frac{5}{3} \]

Now we compare the two:

• Elyse’s recipe provides \(\frac{3}{4}\) cups of concentrate per 1 cup of water.
• Jamir’s recipe provides \(\frac{5}{3}\) cups of concentrate per 1 cup of water.

To compare, we can convert both to decimals for easier comparison:

1. \(\frac{3}{4} = 0.75\)
2. \(\frac{5}{3} \approx 1.67\)

Conclusion: Jamir’s lemonade has a more lemony taste, with approximately \(1.67\) cups of concentrate per cup of water, compared to Elyse’s \(0.75\) cups of concentrate per cup of water.