Elyse and Jamir each make lemonade. Elyse mixes 1

To find out how much lemonade concentrate Elyse needs for 1 cup of water, let's go through the calculations step-by-step.

Step 1: Convert Elyse's recipe measurements to improper fractions.

Elyse mixes:

• \( 1 \frac{7}{3} \) cups of water
• \( 2 \frac{1}{2} \) cups of lemonade concentrate

Convert these to improper fractions:

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

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

Step 2: Calculate how much lemonade concentrate is needed per 1 cup of water.

Now we need to divide the amount of lemonade concentrate by the amount of water: \[ \text{Lemonade concentrate per cup of water} = \frac{\frac{5}{2}}{\frac{10}{3}} \]

Step 3: Rewrite the division as multiplication by the reciprocal.

This can be rewritten as: \[ \frac{5}{2} \times \frac{3}{10} \]

Step 4: Multiply the fractions.

Now, multiply the numerators and the denominators: \[ \frac{5 \times 3}{2 \times 10} = \frac{15}{20} \]

Step 5: Simplify the fraction.

To simplify \( \frac{15}{20} \): \[ \frac{15 \div 5}{20 \div 5} = \frac{3}{4} \]

This means Elyse needs \( \frac{3}{4} \) cups of lemonade concentrate for 1 cup of water.

Summary Table Entry for Elyse:

Elyse's Lemonade Recipe:

• Water (cups): \( 1 \frac{7}{3} \)
• Lemonade Concentrate (cups): \( 2 \frac{1}{2} \)
• Concentrate needed per 1 cup of water: \( \frac{3}{4} \)

Now for Jamir’s lemonade:

We will do the same for Jamir, who mixes:

• \( 1 \frac{3}{1} \) cups of water, which is simply \( 4 \) cups of water (1 is included in the fraction)
• \( 5 \frac{2}{1} \) cups of lemonade concentrate, which is \( 7 \) cups of concentrate.

Convert measurements to improper fractions:

• Water: \( 1 \frac{3}{1} = 4 \)
• Lemonade Concentrate: \( 5 \frac{2}{1} = 7 \)

Calculate how much lemonade concentrate is needed per 1 cup of water:

Now we divide the amount of concentrate by the amount of water: \[ \text{Lemonade concentrate per cup of water} = \frac{7}{4} \]

This means Jamir needs \( \frac{7}{4} \) cups of lemonade concentrate for 1 cup of water.

Summary Table Entry for Jamir:

Jamir's Lemonade Recipe:

• Water (cups): \( 4 \)
• Lemonade Concentrate (cups): \( 7 \)
• Concentrate needed per 1 cup of water: \( \frac{7}{4} \)

Conclusion:

• Elyse’s lemonade concentration per 1 cup of water: \( \frac{3}{4} \)
• Jamir’s lemonade concentration per 1 cup of water: \( \frac{7}{4} \)

Comparison: Jamir's lemonade has a more lemony taste because it has a higher concentration of lemonade concentrate per cup of water.