To find how many cups of lemonade Kate used, you multiply the amount Dustin used by 3 ¾.

Dustin used 5 cups of lemonade, so:

$\text{Kate's lemonade} = 5 \times 3\frac{3}{4}$

First, convert the mixed number $3\frac{3}{4}$ into an improper fraction:

$3\frac{3}{4} = \frac{15}{4}$

Now, multiply:

$5 \times \frac{15}{4} = \frac{5 \times 15}{4} = \frac{75}{4} = 18\frac{3}{4}$

So, Kate used $18\frac{3}{4}$ cups of lemonade.

Answer:

Kate used $18\frac{3}{4}$ cups of lemonade.

Would you like any further clarification?

Here are 5 related questions:

1. If Dustin had used 7 cups of lemonade, how much would Kate have used?
2. What if Kate had used 20 cups of lemonade, how much did Dustin use?
3. How would the equation change if Kate used 2 ½ times as much lemonade as Dustin?
4. If both bowls were combined, how much lemonade would they have together?
5. How do you convert between mixed numbers and improper fractions in general?

Tip: When multiplying by mixed numbers, always convert them into improper fractions first for easier calculations.