i've just started on £600 for 2 days a week, every week allow 3 weeks holiday a year. From jan to july this day rate was £550, a day, increase in July to £600. Also i earn £1500 a month for one client (since beg of year) and £1100 month for another - started this in May. how much have i earned this year? i also earned £550 for 4 days a month Feb - April

Let's break down your earnings and calculate them step by step:

### 1. **Day Rate Earnings (Main Source)**

From **January to June** (before the increase in July), you earned £550 per day for 2 days a week.

- Weeks from **January to June** = 26 weeks.
- Workdays per week = 2.
- Total workdays from January to June = \( 26 \times 2 = 52 \) days.
- Earnings from January to June = \( 52 \times 550 = £28,600 \).

From **July onwards**, you earned £600 per day for 2 days a week.

- Weeks from **July to end of the year** = 26 weeks (same as the first half of the year).
- Total workdays from July to December = \( 26 \times 2 = 52 \) days.
- Earnings from July to December = \( 52 \times 600 = £31,200 \).

#### Subtotal (Main Source): 
- January to June: £28,600
- July to December: £31,200

**Total earnings from your main source** = £28,600 + £31,200 = **£59,800**.

### 2. **Client 1 Earnings (£1,500 per month)**

- You earned £1,500 per month from **January to December**.
- Total earnings from this client = \( 12 \times 1,500 = £18,000 \).

### 3. **Client 2 Earnings (£1,100 per month)**

- You started earning £1,100 per month from **May** onwards.
- Months from May to December = 8 months.
- Total earnings from this client = \( 8 \times 1,100 = £8,800 \).

### 4. **Feb to April Earnings (£550 for 4 days a month)**

- From **February to April**, you earned £550 per day for 4 days a month.
- Total months = 3.
- Total earnings = \( 3 \times 4 \times 550 = £6,600 \).

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### **Total Earnings for the Year**

Now, summing everything up:

- Main source: £59,800
- Client 1: £18,000
- Client 2: £8,800
- Feb–April: £6,600

**Total earnings** = £59,800 + £18,000 + £8,800 + £6,600 = **£93,200**.

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Let me know if you'd like more details or have any questions!

### Related Questions:
1. How will tax affect your total earnings this year?
2. What will be your average monthly income after tax?
3. How would a further rate increase impact your earnings?
4. What if you increased your client work to 3 days a week?
5. How do holiday weeks affect your total earnings?

### Tip:  
If you track your earnings monthly, it helps to predict your year-end income and manage taxes effectively.

Learn how to calculate total yearly earnings when your day rate increases mid-year and you have additional income from multiple clients. This problem involves basic arithmetic and is suitable for students in Grades 9-12.

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