The SQ&L Corporation produces a certain toy at a rate of x units per hour, which they sell for US$...

Phase 1: Owning the Dataset

Understanding the Given Information

We have:

• Production rate: \(\mathrm{x}\) units per hour
• Selling price: US$ \(\mathrm{y}\) per unit
• Time period: 4 hours

Visual Representation

Let's use a simple timeline to visualize the production:

Hour 1      Hour 2      Hour 3      Hour 4
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
x units  →  x units  →  x units  →  x units

Testing with Concrete Numbers

Let's pick simple numbers to verify our understanding:

• If \(\mathrm{x} = 10\) units/hour
• If \(\mathrm{y} = \$5\)/unit
• In 4 hours: \(10 \times 4 = 40\) units produced
• Revenue: \(40 \text{ units} \times \$5/\text{unit} = \$200\)

Phase 2: Understanding the Question

We need to find expressions for:

1. Units produced in 4 hours
2. Revenue from units produced in 4 hours

Breaking Down Each Part

Part 1: Units produced in 4 hours

• This is a straightforward rate × time calculation
• Rate = \(\mathrm{x}\) units/hour
• Time = 4 hours
• Total units = \(\mathrm{x} \times 4 = 4\mathrm{x}\) units

Part 2: Revenue from units produced in 4 hours

• Revenue = (number of units) × (price per unit)
• Number of units produced = \(4\mathrm{x}\)
• Price per unit = \(\mathrm{y}\)
• Revenue = \(4\mathrm{x} \times \mathrm{y} = 4\mathrm{xy}\)

Phase 3: Finding the Answer

Matching to Answer Choices

Our answer choices are: ["4x", "4y", "4xy", "4x/y", "xy/4"]

For Units produced in 4 hours:

• We need \(4\mathrm{x}\)
• Looking at choices: "4x" ✓ (This matches!)

For Revenue from units produced in 4 hours:

• We need \(4\mathrm{xy}\)
• Looking at choices: "4xy" ✓ (This matches!)

Verification with Our Example

• Units: \(4\mathrm{x} = 4(10) = 40\) units ✓
• Revenue: \(4\mathrm{xy} = 4(10)(5) = \$200\) ✓

Phase 4: Solution

Final Answer:

• Statement 1 (Units produced in 4 hours): \(4\mathrm{x}\)
• Statement 2 (Revenue from units produced in 4 hours): \(4\mathrm{xy}\)

These selections follow the fundamental principles:

• Production = rate × time
• Revenue = quantity × price per unit