Let's break down and solve the problem step-by-step:

Given:

• Harley has 6 pints of lemonade.
• Rosie has $3 \frac{2}{3}$ times as many pints of lemonade as Harley.

Part (a): How many pints of lemonade does Rosie have?

1. First, convert $3 \frac{2}{3}$ to an improper fraction: $3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}$

2. Multiply this fraction by the amount of lemonade Harley has: $\text{Rosie’s pints} = 6 \times \frac{11}{3} = \frac{6 \times 11}{3} = \frac{66}{3} = 22$

   Rosie has 22 pints of lemonade.

Part (b): How many more pints of lemonade does Rosie have than Harley?

1. Subtract the amount of lemonade Harley has from the amount Rosie has: $22 - 6 = 16$

   Rosie has 16 more pints of lemonade than Harley.

Final Answers:

• (a) Rosie has 22 pints of lemonade.
• (b) Rosie has 16 more pints of lemonade than Harley.

Would you like a detailed explanation of how these calculations were made or have any questions?

Here are 5 related questions to further expand on this topic:

1. If Harley had 8 pints of lemonade instead, how many pints would Rosie have?
2. What if Rosie had 4 times as many pints as Harley instead of $3 \frac{2}{3}$ times?
3. If Rosie gave 5 pints of lemonade to Harley, how many pints would each have then?
4. How many pints of lemonade would Rosie have if the ratio was instead $2 \frac{1}{2}$ times Harley's amount?
5. Can you represent the situation using an equation involving variables for both Harley's and Rosie's amounts?

Tip: When multiplying mixed numbers by whole numbers, it's often easiest to first convert the mixed number into an improper fraction for straightforward multiplication.