Answer :
Sure, let's tackle this question step-by-step.
### 1.1.1 Write down a formula to represent Chloe's total expenses:
Chloe's total expenses consist of two parts:
- The cost to make each tortilla, which is R5 per tortilla.
- The fixed cost to rent the stall, which is R500.
To create a formula for the total expenses ([tex]\( E \)[/tex]) based on the number of tortillas sold ([tex]\( n \)[/tex]), we can use the following linear equation:
[tex]\[ \text{Total Expenses} = 5n + 500 \][/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'll use the formula from 1.1.1 to calculate the expenses for each quantity of tortillas sold:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of tortillas} & \text{Total Expenses (R)} \\ \hline 0 & 500 \\ 50 & 750 \\ 100 & 1000 \\ 150 & 1250 \\ 200 & 1500 \\ 250 & 1750 \\ \hline \end{array} \][/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 accordingly.
Here is how you can visualize it through explanation:
1. Axes Setup:
- The x-axis represents the number of tortillas sold.
- The y-axis represents the total amount in Rands (income or expenses).
2. Plotting the Income Line:
- Points to plot based on the given table.
- Connect these points with a line to represent Chloe's total income.
3. Plotting the Expenses Line:
- Points to plot based on our previously calculated expenses.
- Connect these points with a line to represent Chloe's total expenses.
Graphical Representation Example:
[tex]\[ \begin{array}{cc} \text{Number of Tortillas} & \text{Total Income and Total Expenses} \\ 0 & \quad (0, 0) \quad \text{Income}, \quad (0, 500) \quad \text{Expenses} \\ 50 & \quad (50, 750) \quad \text{Income}, \quad (50, 750) \quad \text{Expenses} \\ 100 & \quad (100, 1500) \quad \text{Income}, \quad (100, 1000) \quad \text{Expenses} \\ 150 & \quad (150, 2250) \quad \text{Income}, \quad (150, 1250) \quad \text{Expenses} \\ 200 & \quad (200, 3000) \quad \text{Income}, \quad (200, 1500) \quad \text{Expenses} \\ 250 & \quad (250, 3750) \quad \text{Income}, \quad (250, 1750) \quad \text{Expenses} \\ \end{array} \][/tex]
- Income Line: Starts from (0,0) and rises through (50, 750), (100, 1500), (150, 2250), (200, 3000), and (250, 3750).
- Expenses Line: Starts from (0,500) and rises through (50, 750), (100, 1000), (150, 1250), (200, 1500), and (250, 1750).
By plotting these points and drawing the respective lines, you will get two intersecting lines where the income line rises more steeply than the expenses line, showing how Chloe's potential profit increases as more tortillas are sold.
### 1.1.1 Write down a formula to represent Chloe's total expenses:
Chloe's total expenses consist of two parts:
- The cost to make each tortilla, which is R5 per tortilla.
- The fixed cost to rent the stall, which is R500.
To create a formula for the total expenses ([tex]\( E \)[/tex]) based on the number of tortillas sold ([tex]\( n \)[/tex]), we can use the following linear equation:
[tex]\[ \text{Total Expenses} = 5n + 500 \][/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'll use the formula from 1.1.1 to calculate the expenses for each quantity of tortillas sold:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of tortillas} & \text{Total Expenses (R)} \\ \hline 0 & 500 \\ 50 & 750 \\ 100 & 1000 \\ 150 & 1250 \\ 200 & 1500 \\ 250 & 1750 \\ \hline \end{array} \][/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 accordingly.
Here is how you can visualize it through explanation:
1. Axes Setup:
- The x-axis represents the number of tortillas sold.
- The y-axis represents the total amount in Rands (income or expenses).
2. Plotting the Income Line:
- Points to plot based on the given table.
- Connect these points with a line to represent Chloe's total income.
3. Plotting the Expenses Line:
- Points to plot based on our previously calculated expenses.
- Connect these points with a line to represent Chloe's total expenses.
Graphical Representation Example:
[tex]\[ \begin{array}{cc} \text{Number of Tortillas} & \text{Total Income and Total Expenses} \\ 0 & \quad (0, 0) \quad \text{Income}, \quad (0, 500) \quad \text{Expenses} \\ 50 & \quad (50, 750) \quad \text{Income}, \quad (50, 750) \quad \text{Expenses} \\ 100 & \quad (100, 1500) \quad \text{Income}, \quad (100, 1000) \quad \text{Expenses} \\ 150 & \quad (150, 2250) \quad \text{Income}, \quad (150, 1250) \quad \text{Expenses} \\ 200 & \quad (200, 3000) \quad \text{Income}, \quad (200, 1500) \quad \text{Expenses} \\ 250 & \quad (250, 3750) \quad \text{Income}, \quad (250, 1750) \quad \text{Expenses} \\ \end{array} \][/tex]
- Income Line: Starts from (0,0) and rises through (50, 750), (100, 1500), (150, 2250), (200, 3000), and (250, 3750).
- Expenses Line: Starts from (0,500) and rises through (50, 750), (100, 1000), (150, 1250), (200, 1500), and (250, 1750).
By plotting these points and drawing the respective lines, you will get two intersecting lines where the income line rises more steeply than the expenses line, showing how Chloe's potential profit increases as more tortillas are sold.
