Let's solve this step by step.

Luke bought:

• $3 \frac{1}{2}$ pounds of green beans, which equals $3.5$ pounds.
• $1 \frac{1}{4}$ pounds of cucumbers, which equals $1.25$ pounds.

Now, we use the vegetable stand price chart to calculate the total cost:

• Price per pound of green beans = $1.28
• Price per pound of cucumbers = $0.88

Green Beans:

$3.5$ pounds × $1.28 = $4.48$ dollars.

Cucumbers:

$1.25$ pounds × $0.88 = $1.10$ dollars.

Total cost:

$4.48 + 1.10 = 5.58$ dollars.

Luke paid with a $10 bill, so his change will be: $10.00 - 5.58 = 4.42 \text{ dollars}.$

The correct answer should be B ($4.42), not A.

Let me know if you'd like further details, and here are some related questions:

1. How do you calculate fractional weight values when shopping?
2. What is the total cost if Luke bought 2 pounds of carrots instead?
3. If prices increased by 10%, how much would Luke's total be?
4. How do you handle mixed numbers when multiplying with decimals?
5. How would the total change if Luke bought 2 pounds of potatoes instead of green beans?

Tip: Always double-check the unit prices when solving real-life math problems like this!