A real estate agency charges a commission for selling a property. The commission is based on the selling price shown in the table: commission rates (up to $300000 4%) and ($300000 and over 5%) Bailey is paid $180 per week by the real estate agency plus 5% of the commission received by the real estate agency. This week, Bailey sold one property for $290000 and one for $600000. He sold no properties in the last week. A- what is the commission paid to the real estate agency for the $290000 sales? B - what is the commis paid to the real estate agency for both properties? C- calculate baileys pay for this week. D- what is Baileys average weekly income for the two week period?

Let's break down and solve each part of the problem systematically.

### **Given Information:**
- Commission rates:
  - **Up to $300,000:** 4%
  - **$300,000 and over:** 5%
- Bailey's earnings:
  - **Base salary:** $180 per week
  - **Additional:** 5% of the real estate agency's commission

### **Part A: Commission for the $290,000 Sale**
Since the sale price ($290,000) is less than $300,000, the commission rate is **4%**.
- Commission = 4% of $290,000
\[
\text{Commission} = 0.04 \times 290,000 = 11,600
\]

So, the commission paid to the real estate agency for the $290,000 sale is **$11,600**.

### **Part B: Commission for Both Properties**
- **Property 1:** Already calculated as $11,600 (from Part A).
- **Property 2:** Selling price = $600,000. Since this is $300,000 or more, the commission rate is **5%**.
  \[
  \text{Commission} = 0.05 \times 600,000 = 30,000
  \]

- **Total commission for both properties:**
  \[
  11,600 + 30,000 = 41,600
  \]

The commission paid to the real estate agency for both properties is **$41,600**.

### **Part C: Bailey's Pay for This Week**
- **Base salary:** $180
- **Additional commission:** Bailey gets 5% of the real estate agency's total commission ($41,600).
  \[
  \text{Bailey's commission} = 0.05 \times 41,600 = 2,080
  \]

- **Total pay:** 
  \[
  180 + 2,080 = 2,260
  \]

Bailey's pay for this week is **$2,260**.

### **Part D: Bailey's Average Weekly Income Over Two Weeks**
- **Week 1:** No properties were sold, so Bailey only received his base salary of $180.
- **Week 2:** Bailey's pay was $2,260 (calculated in Part C).

- **Total income over two weeks:** 
  \[
  180 + 2,260 = 2,440
  \]

- **Average weekly income:**
  \[
  \frac{2,440}{2} = 1,220
  \]

Bailey's average weekly income for the two-week period is **$1,220**.

---

### Summary of Answers
1. **Part A:** $11,600
2. **Part B:** $41,600
3. **Part C:** $2,260
4. **Part D:** $1,220

Would you like further details or have any questions?

### **5 Related Questions**
1. If Bailey sold another property for $350,000 next week, what would be his total earnings for that week?
2. What would Bailey's weekly pay be if the agency's commission rates changed to 3% for up to $300,000 and 6% for $300,000 and over?
3. How would Bailey's average weekly income change if he sold properties totaling $1,000,000 in a month?
4. How much commission would the real estate agency earn if Bailey sold three properties each worth $250,000?
5. If Bailey receives a 10% commission instead of 5%, what would his earnings be for this week?

### **Tip:** When calculating percentages, remember to convert the percentage to a decimal (e.g., 4% becomes 0.04) before multiplying it by the relevant value.

A real estate agency charges a commission for selling a property. The commission is based on the selling price shown in the table: commission rates (up to $300000 4%) and ($300000 and over 5%). Bailey is paid $180 per week by the real estate agency plus 5% of the commission received by the real estate agency. This week, Bailey sold one property for $290000 and one for $600000. He sold no properties in the last week. A- what is the commission paid to the real estate agency for the $290000 sales? B - what is the commission paid to the real estate agency for both properties? C- calculate Bailey's pay for this week. D- what is Bailey's average weekly income for the two-week period?

Learn how to calculate the commission for a real estate agency and Bailey's weekly income. This problem involves finding the commission from property sales and calculating Bailey's pay based on commission and base salary. Suitable for students in Grades 9-12.

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