1. Determine the number of tour packages at the break-even point. 2. Determine the income if 8 tour packages are sold. 9000 3. Hence calculate the profit made from 6 tour packages sold. Use the formula: Profit = Income - Expenses - VAT payable 4. Determine the number of tour packages that were sold if the expense are R1 500 more than the income

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To tackle the series of questions regarding the tour packages, we'll outline a step-by-step approach for each. However, certain assumptions and additional information are necessary to provide precise numerical answers. Here's how you can proceed:

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### **Understanding the Given Information**

1. **Income from Tour Packages:**
   - **8 tour packages** sold generate an **income of R9,000**.
   - **Income per package (I_p)** = Total Income / Number of Packages = R9,000 / 8 = **R1,125** per package.

2. **Profit Formula:**
   - **Profit (P)** = **Income (I)** - **Expenses (E)** - **VAT Payable (VAT)**
   - **VAT:** Assuming a standard VAT rate (e.g., **15%**), VAT payable can be calculated as **VAT = 15% of Income (I)**.

3. **Expenses Structure:**
   - Typically, expenses consist of **fixed costs (F)** and **variable costs per package (C_v)**.
   - **Total Expenses (E)** = **Fixed Costs (F)** + (**Variable Cost per Package (C_v)** × **Number of Packages (x)**)

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### **1. Determining the Break-Even Point**

**Break-Even Point** occurs when **Profit (P)** is **zero**.

- **Formula:**  
  $$ P = I - E - VAT = 0 $$  
  $$ I = E + VAT $$

- **Calculations:**  
  - **Income (I):** $$ I = 1,125x $$  
  - **VAT:** $$ VAT = 0.15 	imes I = 0.15 	imes 1,125x = 168.75x $$  
  - **Expenses (E):** $$ E = F + C_vx $$

- **Setting Up the Equation:**  
  $$ 1,125x = F + C_vx + 168.75x $$  
  $$ 1,125x - C_vx - 168.75x = F $$  
  $$ (956.25 - C_v)x = F $$

- **Solving for x (Break-Even Point):**  
  $$ x = \frac{F}{956.25 - C_v} $$

**Note:** To find a numerical value for $$ x $$, you need to know the **fixed costs (F)** and the **variable cost per package (C_v)**.

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### **2. Income When 8 Tour Packages Are Sold**

- **Given:**  
  - **Number of Packages (x):** 8  
  - **Income (I):** R9,000

- **Income per Package:**  
  $$ I_p = \frac{9,000}{8} = R1,125 $$ per package

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### **3. Calculating Profit from 6 Tour Packages Sold**

- **Given:**  
  - **Number of Packages (x):** 6  
  - **Income (I):** $$ I = 1,125 	imes 6 = R6,750 $$

- **Expenses (E):**  
  Without specific values for **fixed costs (F)** and **variable costs (C_v)**, we can express expenses as:  
  $$ E = F + C_v 	imes 6 $$

- **VAT Payable:**  
  $$ VAT = 0.15 	imes 6,750 = R1,012.50 $$

- **Profit Formula:**  
  $$ P = I - E - VAT $$  
  $$ P = 6,750 - (F + 6C_v) - 1,012.50 $$  
  $$ P = 5,737.50 - F - 6C_v $$

**Note:** To determine the exact profit, values for **F** and **C_v** are required.

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### **4. Determining Number of Packages Sold When Expenses Exceed Income by R1,500**

- **Given:**  
  - **Expenses exceed Income by R1,500:**  
    $$ E = I + 1,500 $$

- **Expressing in Terms of Packages (x):**  
  $$ F + C_vx = 1,125x + 1,500 $$

- **Solving for x:**  
  $$ F + C_vx - 1,125x = 1,500 $$  
  $$ F + (C_v - 1,125)x = 1,500 $$  
  $$ (C_v - 1,125)x = 1,500 - F $$  
  $$ x = \frac{1,500 - F}{C_v - 1,125} $$

**Note:** This equation requires knowledge of both **fixed costs (F)** and **variable cost per package (C_v)** to solve for $$ x $$.

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### **Summary and Additional Requirements**

To provide precise numerical answers to all the questions, the following additional information is necessary:

1. **Fixed Costs (F):** The total fixed expenses irrespective of the number of packages sold.
2. **Variable Cost per Package (C_v):** Expenses that vary directly with the number of packages sold.
3. **VAT Rate:** Assumed here as 15%, but confirm if different.

**Recommendation:** Please provide the fixed costs and variable cost per package to enable accurate calculations. If the VAT rate is different from the assumed 15%, kindly specify the correct rate.

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By supplying the additional required data, we can proceed to compute the exact break-even point, profit from 6 packages, and the number of packages sold when expenses exceed income by R1,500.
To determine the number of tour packages at the break-even point, income from 8 packages, profit from 6 packages, and the number of packages sold when expenses exceed income by R1,500, you need to provide the fixed costs and variable cost per package. With that information, we can calculate the exact numbers using the given formulas.

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