This worksheet helps students practice calculating commission earnings and total gross wages based on sales figures.

Let's solve each problem step by step.

---

Problem 1: Cara's Commission and Gross Wage

Given:
- Basic wage: $140 per week
- Commission rate: 5% on the value of goods sold
- Sales amount: $1525

#### Step 1: Calculate the commission
The commission is calculated as:
\[
\text{Commission} = \text{Sales amount} \times \text{Commission rate}
\]
\[
\text{Commission} = 1525 \times 0.05 = 76.25
\]

So, Cara's commission is:
\[
\boxed{76.25}
\]

#### Step 2: Calculate the gross wage
The gross wage is the sum of the basic wage and the commission:
\[
\text{Gross wage} = \text{Basic wage} + \text{Commission}
\]
\[
\text{Gross wage} = 140 + 76.25 = 216.25
\]

So, Cara's gross wage is:
\[
\boxed{216.25}
\]

---

Problem 2: Videsh's Commission and Gross Wage

Given:
- Basic wage: $225 per week
- Commission rate: 3% on the value of goods sold above $5000
- Sales amount: $12500

#### Step 1: Determine the sales amount eligible for commission
Videsh only earns a commission on the sales amount above $5000. So, we calculate:
\[
\text{Eligible sales for commission} = \text{Total sales} - 5000
\]
\[
\text{Eligible sales for commission} = 12500 - 5000 = 7500
\]

#### Step 2: Calculate the commission
The commission is calculated as:
\[
\text{Commission} = \text{Eligible sales for commission} \times \text{Commission rate}
\]
\[
\text{Commission} = 7500 \times 0.03 = 225
\]

So, Videsh's commission is:
\[
\boxed{225}
\]

#### Step 3: Calculate the gross wage
The gross wage is the sum of the basic wage and the commission:
\[
\text{Gross wage} = \text{Basic wage} + \text{Commission}
\]
\[
\text{Gross wage} = 225 + 225 = 450
\]

So, Videsh's gross wage is:
\[
\boxed{450}
\]

---

Problem 3: Nathan's Commission and Total Sales

Given:
- Total earnings: $646
- Basic wage: $475
- Commission rate: 2.5% of the total value of goods sold

#### Step 1: Calculate the commission
Nathan's total earnings are the sum of his basic wage and his commission. Let \( C \) be the commission. Then:
\[
\text{Total earnings} = \text{Basic wage} + \text{Commission}
\]
\[
646 = 475 + C
\]
Solving for \( C \):
\[
C = 646 - 475 = 171
\]

So, Nathan's commission is:
\[
\boxed{171}
\]

#### Step 2: Calculate the total value of goods sold
The commission is 2.5% of the total value of goods sold. Let \( S \) be the total value of goods sold. Then:
\[
\text{Commission} = \text{Total value of goods sold} \times \text{Commission rate}
\]
\[
171 = S \times 0.025
\]
Solving for \( S \):
\[
S = \frac{171}{0.025} = 6840
\]

So, the total value of the goods sold is:
\[
\boxed{6840}
\]

---

Final Answers:

1. Cara's commission: \(\boxed{76.25}\)
Cara's gross wage: \(\boxed{216.25}\)

2. Videsh's commission: \(\boxed{225}\)
Videsh's gross wage: \(\boxed{450}\)

3. (a) Nathan's commission: \(\boxed{171}\)
(b) Total value of goods sold: \(\boxed{6840}\)