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To solve this problem, we'll go through each sub-question step by step.
### 1.1.1 Write down a formula to represent Chloe's total expenses
Chloe's total expenses consist of a fixed stall renting cost and the cost of making tortillas. We can write this as:
[tex]\[ \text{Total Expenses} = \text{Fixed Cost} + (\text{Cost per Tortilla} \times \text{Number of Tortillas}) \][/tex]
Given:
- The fixed cost is R500.
- The cost per tortilla is R5.
Therefore, the formula becomes:
[tex]\[ \text{Total Expenses} = 500 + 5 \times (\text{Number of Tortillas}) \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas
Using the formula from 1.1.1, we calculate the total expenses for different numbers of tortillas.
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of tortillas} & \text{Total Expenses (R)} \\ \hline 0 & 500 \\ \hline 50 & 750 \\ \hline 100 & 1000 \\ \hline 150 & 1250 \\ \hline 200 & 1500 \\ \hline 250 & 1750 \\ \hline \end{array} \][/tex]
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even
To find the break-even point, we look for the number of tortillas where total income equals total expenses.
Given:
- Total income for 50 tortillas is R750.
- Total expenses for 50 tortillas is R750.
Since the total income and total expenses are equal at 50 tortillas, Chloe breaks even when she sells 50 tortillas.
Hence, the minimum number of tortillas Chloe must sell to break even is:
[tex]\[ 50 \text{ tortillas} \][/tex]
### 1.1.5 Chloe sold 240 tortillas. Complete the income and expense statement
First, let's calculate the total income, total expenses, and profit for selling 240 tortillas.
Total Income:
[tex]\[ \text{Total Income} = \text{Selling Price per Tortilla} \times \text{Number of Tortillas} \][/tex]
[tex]\[ \text{Total Income} = 15 \times 240 = 3600 \text{ R} \][/tex]
Total Expenses:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 240 = 500 + 1200 = 1700 \text{ R} \][/tex]
Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} \][/tex]
[tex]\[ \text{Profit} = 3600 - 1700 = 1900 \text{ R} \][/tex]
The completed income and expense statement is:
[tex]\[ \begin{array}{|c|c|c|} \hline \multicolumn{2}{|c|}{\text{Income}} & \text{Expense} \\ \hline \text{Sale of 240 tortillas} & 3600 & \text{Fixed cost} = 500 \\ \hline & & \text{Cost of each tortilla} = 5 \times 240 = 1200 \\ \hline \text{Total Income} & 3600 & \text{Total Cost of 240 tortillas} = 1700 \\ \hline & & \text{Profit} = 1900 \\ \hline \end{array} \][/tex]
This comprehensive breakdown provides all the necessary details as required by the question.
### 1.1.1 Write down a formula to represent Chloe's total expenses
Chloe's total expenses consist of a fixed stall renting cost and the cost of making tortillas. We can write this as:
[tex]\[ \text{Total Expenses} = \text{Fixed Cost} + (\text{Cost per Tortilla} \times \text{Number of Tortillas}) \][/tex]
Given:
- The fixed cost is R500.
- The cost per tortilla is R5.
Therefore, the formula becomes:
[tex]\[ \text{Total Expenses} = 500 + 5 \times (\text{Number of Tortillas}) \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas
Using the formula from 1.1.1, we calculate the total expenses for different numbers of tortillas.
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of tortillas} & \text{Total Expenses (R)} \\ \hline 0 & 500 \\ \hline 50 & 750 \\ \hline 100 & 1000 \\ \hline 150 & 1250 \\ \hline 200 & 1500 \\ \hline 250 & 1750 \\ \hline \end{array} \][/tex]
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even
To find the break-even point, we look for the number of tortillas where total income equals total expenses.
Given:
- Total income for 50 tortillas is R750.
- Total expenses for 50 tortillas is R750.
Since the total income and total expenses are equal at 50 tortillas, Chloe breaks even when she sells 50 tortillas.
Hence, the minimum number of tortillas Chloe must sell to break even is:
[tex]\[ 50 \text{ tortillas} \][/tex]
### 1.1.5 Chloe sold 240 tortillas. Complete the income and expense statement
First, let's calculate the total income, total expenses, and profit for selling 240 tortillas.
Total Income:
[tex]\[ \text{Total Income} = \text{Selling Price per Tortilla} \times \text{Number of Tortillas} \][/tex]
[tex]\[ \text{Total Income} = 15 \times 240 = 3600 \text{ R} \][/tex]
Total Expenses:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 240 = 500 + 1200 = 1700 \text{ R} \][/tex]
Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} \][/tex]
[tex]\[ \text{Profit} = 3600 - 1700 = 1900 \text{ R} \][/tex]
The completed income and expense statement is:
[tex]\[ \begin{array}{|c|c|c|} \hline \multicolumn{2}{|c|}{\text{Income}} & \text{Expense} \\ \hline \text{Sale of 240 tortillas} & 3600 & \text{Fixed cost} = 500 \\ \hline & & \text{Cost of each tortilla} = 5 \times 240 = 1200 \\ \hline \text{Total Income} & 3600 & \text{Total Cost of 240 tortillas} = 1700 \\ \hline & & \text{Profit} = 1900 \\ \hline \end{array} \][/tex]
This comprehensive breakdown provides all the necessary details as required by the question.
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