Answer :
Alright, let's go through each part of the question step-by-step:
### 1.1.1 Write down a formula to represent Chloe's total expenses:
Chloe's total expenses comprise a fixed cost of R500 for renting the stall, plus an additional variable cost of R5 for each tortilla she makes. Therefore, the formula to represent Chloe's total expenses ([tex]\(E\)[/tex]) when she sells [tex]\(n\)[/tex] tortillas is:
[tex]\[ \text{Total Expenses} = 500 + 5n \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas:
Use the formula from 1.1.1 to calculate the expenses for each number of tortillas.
| Number of tortillas | Total Expenses (R) |
|---------------------|--------------------|
| 0 | 500 |
| 50 | 750 |
| 100 | 1000 |
| 150 | 1250 |
| 200 | 1500 |
| 250 | 1750 |
### 1.1.3 Draw a Line Graph:
On the provided annexure:
- Plot the total income for different numbers of tortillas using the given table:
- Income when selling [tex]\( n \)[/tex] tortillas: [tex]\( \text{Total Income} = 15n \)[/tex]
- Use the table values: (0, 0), (50, 750), (100, 1500), (150, 2250), (200, 3000), (250, 3750)
- Plot the total expenses using the table calculated in 1.1.2:
- Expenses when selling [tex]\( n \)[/tex] tortillas: [tex]\( \text{Total Expenses} = 500 + 5n \)[/tex]
- Use the table values: (0, 500), (50, 750), (100, 1000), (150, 1250), (200, 1500), (250, 1750)
Draw these points and connect them with lines, clearly labeling the graphs as "Total Income" and "Total Expenses."
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even:
- Break-even occurs when total income equals total expenses:
[tex]\[ 15n = 500 + 5n \][/tex]
Subtract 5n from both sides:
[tex]\[ 10n = 500 \][/tex]
Divide by 10:
[tex]\[ n = 50 \][/tex]
Therefore, Chloe must sell at least 50 tortillas to break even.
### 1.1.5 Chloe sold 240 tortillas. Complete the income and expense statement for the sale of 240 tortillas and calculate the profit:
Income:
- Sale of 240 tortillas:
[tex]\[ \text{Total Income} = 240 \times 15 = 3600 \text{R} \][/tex]
Expenses:
- Fixed cost for renting the stall: 500 R
- Cost of each tortilla ([tex]\(5 \text{R} \times 240\)[/tex]):
[tex]\[ \text{Total Cost of 240 tortillas} = 240 \times 5 = 1200 \text{R} \][/tex]
Add the fixed cost to the variable cost:
[tex]\[ \text{Total Expenses} = 500 + 1200 = 1700 \text{R} \][/tex]
Profit:
- Profit is calculated as:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} \][/tex]
[tex]\[ \text{Profit} = 3600 - 1700 = 1900 \text{R} \][/tex]
So, Chloe's income and expense statement for selling 240 tortillas is as follows:
| | Income (R) | Expense (R) |
|---------------|------------|-------------|
| Sale of 240 tortillas | 3600 | Fixed cost: 500 |
| | | Cost of each tortilla: 1200 |
| Total Income | 3600 | Total Cost of 240 tortillas: 1700 |
| | | Profit: 1900 |
Chloe made a profit of R1900 from selling 240 tortillas.
### 1.1.1 Write down a formula to represent Chloe's total expenses:
Chloe's total expenses comprise a fixed cost of R500 for renting the stall, plus an additional variable cost of R5 for each tortilla she makes. Therefore, the formula to represent Chloe's total expenses ([tex]\(E\)[/tex]) when she sells [tex]\(n\)[/tex] tortillas is:
[tex]\[ \text{Total Expenses} = 500 + 5n \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas:
Use the formula from 1.1.1 to calculate the expenses for each number of tortillas.
| Number of tortillas | Total Expenses (R) |
|---------------------|--------------------|
| 0 | 500 |
| 50 | 750 |
| 100 | 1000 |
| 150 | 1250 |
| 200 | 1500 |
| 250 | 1750 |
### 1.1.3 Draw a Line Graph:
On the provided annexure:
- Plot the total income for different numbers of tortillas using the given table:
- Income when selling [tex]\( n \)[/tex] tortillas: [tex]\( \text{Total Income} = 15n \)[/tex]
- Use the table values: (0, 0), (50, 750), (100, 1500), (150, 2250), (200, 3000), (250, 3750)
- Plot the total expenses using the table calculated in 1.1.2:
- Expenses when selling [tex]\( n \)[/tex] tortillas: [tex]\( \text{Total Expenses} = 500 + 5n \)[/tex]
- Use the table values: (0, 500), (50, 750), (100, 1000), (150, 1250), (200, 1500), (250, 1750)
Draw these points and connect them with lines, clearly labeling the graphs as "Total Income" and "Total Expenses."
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even:
- Break-even occurs when total income equals total expenses:
[tex]\[ 15n = 500 + 5n \][/tex]
Subtract 5n from both sides:
[tex]\[ 10n = 500 \][/tex]
Divide by 10:
[tex]\[ n = 50 \][/tex]
Therefore, Chloe must sell at least 50 tortillas to break even.
### 1.1.5 Chloe sold 240 tortillas. Complete the income and expense statement for the sale of 240 tortillas and calculate the profit:
Income:
- Sale of 240 tortillas:
[tex]\[ \text{Total Income} = 240 \times 15 = 3600 \text{R} \][/tex]
Expenses:
- Fixed cost for renting the stall: 500 R
- Cost of each tortilla ([tex]\(5 \text{R} \times 240\)[/tex]):
[tex]\[ \text{Total Cost of 240 tortillas} = 240 \times 5 = 1200 \text{R} \][/tex]
Add the fixed cost to the variable cost:
[tex]\[ \text{Total Expenses} = 500 + 1200 = 1700 \text{R} \][/tex]
Profit:
- Profit is calculated as:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} \][/tex]
[tex]\[ \text{Profit} = 3600 - 1700 = 1900 \text{R} \][/tex]
So, Chloe's income and expense statement for selling 240 tortillas is as follows:
| | Income (R) | Expense (R) |
|---------------|------------|-------------|
| Sale of 240 tortillas | 3600 | Fixed cost: 500 |
| | | Cost of each tortilla: 1200 |
| Total Income | 3600 | Total Cost of 240 tortillas: 1700 |
| | | Profit: 1900 |
Chloe made a profit of R1900 from selling 240 tortillas.