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Sagot :
Let's break down the solution to each part of the question step by step.
### 1.1.1 Write down a formula to represent Chloe's total expenses:
To represent Chloe's total expenses, we need to account for both the fixed cost of renting the stall and the variable cost of making each tortilla.
- Fixed cost: R500
- Variable cost per tortilla: R5
Let [tex]\( x \)[/tex] be the number of tortillas sold. The formula for the total expenses ([tex]\( E \)[/tex]) can be written as:
[tex]\[ E = 500 + 5x \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas:
We use the formula [tex]\( E = 500 + 5x \)[/tex] to calculate the total expenses for different quantities of tortillas sold.
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Number of Tortillas} & \text{Total Expenses (R)} \\ \hline 0 & 500 \\ 50 & 750 \\ 100 & 1000 \\ 150 & 1250 \\ 200 & 1500 \\ 250 & 1750 \\ \hline \end{tabular} \][/tex]
### 1.1.3 Use Annexure A to draw, on the same set of axes, a line graph representing Chloe's total income and another line representing her expenses. Label the graphs:
To create this graph:
- Plot the number of tortillas sold on the x-axis.
- Plot the total income and total expenses on the y-axis.
Let's use the data we've calculated:
- Income: [tex]\([0, 750, 1500, 2250, 3000, 3750]\)[/tex]
- Expenses: [tex]\([500, 750, 1000, 1250, 1500, 1750]\)[/tex]
You would draw two lines:
- The line for total income will start at (0, 0) and go through (50, 750), (100, 1500), etc.
- The line for total expenses will start at (0, 500) and go through (50, 750), (100, 1000), etc.
Make sure to label each line clearly on your graph.
### 1.1.4 Chloe sold 240 tortillas. Complete the income and expense statement on the ANNEXURE PROVIDED for the sale of 240 tortillas and show how much profit she made.
Let's calculate the elements required:
1. Income from selling 240 tortillas:
[tex]\[ \text{Income} = 15 \times 240 = R3600 \][/tex]
2. Total Expenses for 240 tortillas:
- Fixed Cost: R500
- Cost of each tortilla: [tex]\( 5 \times 240 = R1200 \)[/tex]
- Total Cost: [tex]\( 500 + 1200 = R1700 \)[/tex]
3. Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} = 3600 - 1700 = R1900 \][/tex]
The completed income and expense statement will be:
[tex]\[ \begin{tabular}{|l|l|l|} \hline \multicolumn{1}{|c|}{ Income } & \multicolumn{1}{|c|}{ Expense } \\ \hline \begin{tabular}{l} Sale of \\ 240 tortillas \end{tabular} & & Fixed cost & R500 \\ \hline & \begin{tabular}{l} Cost of each \\ tortilla \end{tabular} & R1200 \\ \hline Total Income & R3600 & Total Cost of 240 tortillas & R1700 \\ \hline & Profit & R1900 \\ \hline \end{tabular} \][/tex]
This completes all parts of the question.
### 1.1.1 Write down a formula to represent Chloe's total expenses:
To represent Chloe's total expenses, we need to account for both the fixed cost of renting the stall and the variable cost of making each tortilla.
- Fixed cost: R500
- Variable cost per tortilla: R5
Let [tex]\( x \)[/tex] be the number of tortillas sold. The formula for the total expenses ([tex]\( E \)[/tex]) can be written as:
[tex]\[ E = 500 + 5x \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas:
We use the formula [tex]\( E = 500 + 5x \)[/tex] to calculate the total expenses for different quantities of tortillas sold.
[tex]\[ \begin{tabular}{|c|c|} \hline \text{Number of Tortillas} & \text{Total Expenses (R)} \\ \hline 0 & 500 \\ 50 & 750 \\ 100 & 1000 \\ 150 & 1250 \\ 200 & 1500 \\ 250 & 1750 \\ \hline \end{tabular} \][/tex]
### 1.1.3 Use Annexure A to draw, on the same set of axes, a line graph representing Chloe's total income and another line representing her expenses. Label the graphs:
To create this graph:
- Plot the number of tortillas sold on the x-axis.
- Plot the total income and total expenses on the y-axis.
Let's use the data we've calculated:
- Income: [tex]\([0, 750, 1500, 2250, 3000, 3750]\)[/tex]
- Expenses: [tex]\([500, 750, 1000, 1250, 1500, 1750]\)[/tex]
You would draw two lines:
- The line for total income will start at (0, 0) and go through (50, 750), (100, 1500), etc.
- The line for total expenses will start at (0, 500) and go through (50, 750), (100, 1000), etc.
Make sure to label each line clearly on your graph.
### 1.1.4 Chloe sold 240 tortillas. Complete the income and expense statement on the ANNEXURE PROVIDED for the sale of 240 tortillas and show how much profit she made.
Let's calculate the elements required:
1. Income from selling 240 tortillas:
[tex]\[ \text{Income} = 15 \times 240 = R3600 \][/tex]
2. Total Expenses for 240 tortillas:
- Fixed Cost: R500
- Cost of each tortilla: [tex]\( 5 \times 240 = R1200 \)[/tex]
- Total Cost: [tex]\( 500 + 1200 = R1700 \)[/tex]
3. Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} = 3600 - 1700 = R1900 \][/tex]
The completed income and expense statement will be:
[tex]\[ \begin{tabular}{|l|l|l|} \hline \multicolumn{1}{|c|}{ Income } & \multicolumn{1}{|c|}{ Expense } \\ \hline \begin{tabular}{l} Sale of \\ 240 tortillas \end{tabular} & & Fixed cost & R500 \\ \hline & \begin{tabular}{l} Cost of each \\ tortilla \end{tabular} & R1200 \\ \hline Total Income & R3600 & Total Cost of 240 tortillas & R1700 \\ \hline & Profit & R1900 \\ \hline \end{tabular} \][/tex]
This completes all parts of the question.
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