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Sagot :
Let's walk through each part of the problem 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 cost of making each tortilla and the fixed rental cost for the stall.
- Cost of making one tortilla = R5
- Stall rental cost = R500
If we let [tex]\( x \)[/tex] be the number of tortillas sold, then the total expense, [tex]\( E \)[/tex], can be calculated as follows:
[tex]\[ \text{Total Expenses} = 5x + 500 \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas:
Using the formula we derived in 1.1.1 ([tex]\( E = 5x + 500 \)[/tex]), let's calculate the expenses for each given number of tortillas:
[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:
To create the line graph, we use the following data points:
- Total Income (already given):
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of tortillas} & \text{Total Income} (R) \\ \hline 0 & 0 \\ 50 & 750 \\ 100 & 1500 \\ 150 & 2250 \\ 200 & 3000 \\ 250 & 3750 \\ \hline \end{array} \][/tex]
- Total Expenses (calculated in 1.1.2):
[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]
(You will plot these points on the graph, with the number of tortillas on the x-axis and the amount of money (R) on the y-axis, drawing lines through the points for both income and expenses).
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even:
The break-even point is when Chloe's total income equals her total expenses.
Let's set the total income formula [tex]\( I = 15x \)[/tex] equal to the total expense formula [tex]\( E = 5x + 500 \)[/tex] to find the break-even point:
[tex]\[ 15x = 5x + 500 \][/tex]
[tex]\[ 10x = 500 \][/tex]
[tex]\[ x = 50 \][/tex]
Chloe must sell at least 50 tortillas to break even.
### 1.1.5 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:
For 240 tortillas:
- Total Income:
[tex]\[ I = 15 \times 240 = 3600 \text{ R} \][/tex]
- Total Expenses:
[tex]\[ E = 5 \times 240 + 500 = 1700 \text{ R} \][/tex]
- Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} = 3600 - 1700 = 1900 \text{ R} \][/tex]
So, Chloe's profit after selling 240 tortillas is R1900.
### 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 cost of making each tortilla and the fixed rental cost for the stall.
- Cost of making one tortilla = R5
- Stall rental cost = R500
If we let [tex]\( x \)[/tex] be the number of tortillas sold, then the total expense, [tex]\( E \)[/tex], can be calculated as follows:
[tex]\[ \text{Total Expenses} = 5x + 500 \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas:
Using the formula we derived in 1.1.1 ([tex]\( E = 5x + 500 \)[/tex]), let's calculate the expenses for each given number of tortillas:
[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:
To create the line graph, we use the following data points:
- Total Income (already given):
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of tortillas} & \text{Total Income} (R) \\ \hline 0 & 0 \\ 50 & 750 \\ 100 & 1500 \\ 150 & 2250 \\ 200 & 3000 \\ 250 & 3750 \\ \hline \end{array} \][/tex]
- Total Expenses (calculated in 1.1.2):
[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]
(You will plot these points on the graph, with the number of tortillas on the x-axis and the amount of money (R) on the y-axis, drawing lines through the points for both income and expenses).
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even:
The break-even point is when Chloe's total income equals her total expenses.
Let's set the total income formula [tex]\( I = 15x \)[/tex] equal to the total expense formula [tex]\( E = 5x + 500 \)[/tex] to find the break-even point:
[tex]\[ 15x = 5x + 500 \][/tex]
[tex]\[ 10x = 500 \][/tex]
[tex]\[ x = 50 \][/tex]
Chloe must sell at least 50 tortillas to break even.
### 1.1.5 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:
For 240 tortillas:
- Total Income:
[tex]\[ I = 15 \times 240 = 3600 \text{ R} \][/tex]
- Total Expenses:
[tex]\[ E = 5 \times 240 + 500 = 1700 \text{ R} \][/tex]
- Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} = 3600 - 1700 = 1900 \text{ R} \][/tex]
So, Chloe's profit after selling 240 tortillas is R1900.
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