Answer :
Let's solve each part of the question step by step.
### 1.1.1 Write down a formula to represent Chloe's total expenses:
Chloe has two main costs: the cost of making each tortilla and the fixed cost of renting the stall. Given that it costs R8 to make one tortilla and R500 to rent the stall, the total expenses can be represented as follows:
[tex]\[ \text{Total Expenses} = (8 \times \text{number of tortillas}) + 500 \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells [tex]\(0, 50, 100, 150, 200,\)[/tex] and [tex]\(250\)[/tex] tortillas.
We can calculate the total expenses for each quantity of tortillas using the formula from part 1.1.1. Here is the table for Chloe's expenses:
| Number of Tortillas | Total Expenses |
|---------------------|----------------|
| 0 | 500 |
| 50 | 900 |
| 100 | 1300 |
| 150 | 1700 |
| 200 | 2100 |
| 250 | 2500 |
### 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.
Based on the given information and the above table, we have the following:
Total Income:
| Number of Tortillas | Total Income |
|---------------------|--------------|
| 0 | 0 |
| 50 | 750 |
| 100 | 1500 |
| 150 | 2250 |
| 200 | 3000 |
| 250 | 3750 |
We can plot these points on a graph where the x-axis represents the number of tortillas sold, and the y-axis represents the amount of money.
- For total income, plot points at (0,0), (50,750), (100,1500), (150,2250), (200,3000), and (250,3750).
- For total expenses, plot points at (0,500), (50,900), (100,1300), (150,1700), (200,2100), and (250,2500).
Connect the points for each set to form two lines: one for income and one for expenses.
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even.
To determine the break-even point, we need to find the number of tortillas where total income equals total expenses.
From our formula:
[tex]\[ \text{Total Income} = 15 \times \text{number of tortillas} \][/tex]
[tex]\[ \text{Total Expenses} = (8 \times \text{number of tortillas}) + 500 \][/tex]
Set the two equal to each other to find the break-even point:
[tex]\[ 15 \times \text{number of tortillas} = 8 \times \text{number of tortillas} + 500 \][/tex]
[tex]\[ 15T = 8T + 500 \][/tex]
[tex]\[ 7T = 500 \][/tex]
[tex]\[ T = \frac{500}{7} \approx 71.43 \][/tex]
Since Chloe can't sell a fraction of a tortilla, she must sell at least 72 tortillas to break even.
### 1.1.5 Chloe sold 240 tortillas. Complete the income and expense statement for the sale of 240 tortillas and show how much profit she made.
Total Income for 240 tortillas:
[tex]\[ \text{Total Income} = 15 \times 240 = 3600 \][/tex]
Total Expenses for 240 tortillas:
[tex]\[ \text{Total Expenses} = (8 \times 240) + 500 = 1920 + 500 = 2420 \][/tex]
Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} = 3600 - 2420 = 1180 \][/tex]
So, Chloe made a profit of R1180 by selling 240 tortillas.
### 1.1.1 Write down a formula to represent Chloe's total expenses:
Chloe has two main costs: the cost of making each tortilla and the fixed cost of renting the stall. Given that it costs R8 to make one tortilla and R500 to rent the stall, the total expenses can be represented as follows:
[tex]\[ \text{Total Expenses} = (8 \times \text{number of tortillas}) + 500 \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells [tex]\(0, 50, 100, 150, 200,\)[/tex] and [tex]\(250\)[/tex] tortillas.
We can calculate the total expenses for each quantity of tortillas using the formula from part 1.1.1. Here is the table for Chloe's expenses:
| Number of Tortillas | Total Expenses |
|---------------------|----------------|
| 0 | 500 |
| 50 | 900 |
| 100 | 1300 |
| 150 | 1700 |
| 200 | 2100 |
| 250 | 2500 |
### 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.
Based on the given information and the above table, we have the following:
Total Income:
| Number of Tortillas | Total Income |
|---------------------|--------------|
| 0 | 0 |
| 50 | 750 |
| 100 | 1500 |
| 150 | 2250 |
| 200 | 3000 |
| 250 | 3750 |
We can plot these points on a graph where the x-axis represents the number of tortillas sold, and the y-axis represents the amount of money.
- For total income, plot points at (0,0), (50,750), (100,1500), (150,2250), (200,3000), and (250,3750).
- For total expenses, plot points at (0,500), (50,900), (100,1300), (150,1700), (200,2100), and (250,2500).
Connect the points for each set to form two lines: one for income and one for expenses.
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even.
To determine the break-even point, we need to find the number of tortillas where total income equals total expenses.
From our formula:
[tex]\[ \text{Total Income} = 15 \times \text{number of tortillas} \][/tex]
[tex]\[ \text{Total Expenses} = (8 \times \text{number of tortillas}) + 500 \][/tex]
Set the two equal to each other to find the break-even point:
[tex]\[ 15 \times \text{number of tortillas} = 8 \times \text{number of tortillas} + 500 \][/tex]
[tex]\[ 15T = 8T + 500 \][/tex]
[tex]\[ 7T = 500 \][/tex]
[tex]\[ T = \frac{500}{7} \approx 71.43 \][/tex]
Since Chloe can't sell a fraction of a tortilla, she must sell at least 72 tortillas to break even.
### 1.1.5 Chloe sold 240 tortillas. Complete the income and expense statement for the sale of 240 tortillas and show how much profit she made.
Total Income for 240 tortillas:
[tex]\[ \text{Total Income} = 15 \times 240 = 3600 \][/tex]
Total Expenses for 240 tortillas:
[tex]\[ \text{Total Expenses} = (8 \times 240) + 500 = 1920 + 500 = 2420 \][/tex]
Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} = 3600 - 2420 = 1180 \][/tex]
So, Chloe made a profit of R1180 by selling 240 tortillas.
