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QUESTION I

A food fair is going to be held at Zoo Lake. Chloe decides to set up a stall selling tortillas. It costs Chloe R5 to make a tortilla and R500 to rent the stall. She sells each tortilla for R15.

The table below shows the income that Chloe will make if she sells the tortillas:

[tex]\[
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
Number of tortillas & 0 & 50 & 100 & 150 & 200 & 250 \\
\hline
Total Income (R) & 0 & 750 & 1500 & 2250 & 3000 & 3750 \\
\hline
\end{tabular}
\][/tex]

1.1.1 Write down a formula to represent Chloe's total expenses:
[tex]\[ \text{Total Expenses} = \][/tex]

1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas.

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.

1.1.4 Determine the minimum number of tortillas that Chloe must sell in order 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.
```



Answer :

GinnyAnswer
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.

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