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Question 1:
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:
\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}

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

\begin{tabular}{|c|c|}
\hline Income & Expense \\
\hline \begin{tabular}{l}
Sale of \\
240 tortillas
\end{tabular} & Fixed cost \\
\hline & \begin{tabular}{l}
Cost of each \\
tortilla
\end{tabular} \\
\hline Total Income & Total Cost of 240 tortillas \\
\hline & Profit \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Certainly! 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:
The total expenses for Chloe include a fixed cost of renting the stall and the variable cost of making the tortillas. Chloe's total expenses can be represented by the formula:
[tex]\[ \text{Total Expenses} = \text{Fixed Cost} + (\text{Cost per Tortilla} \times \text{Number of Tortillas}) \][/tex]
Given that the fixed cost is R500 and the cost per tortilla is R5, the formula becomes:
[tex]\[ \text{Total Expenses} = 500 + 5 \times \text{Number of Tortillas} \][/tex]

### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas.
Now, we will calculate the total expenses for each given number of tortillas:
- For 0 tortillas:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 0 = 500 \][/tex]
- For 50 tortillas:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 50 = 750 \][/tex]
- For 100 tortillas:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 100 = 1000 \][/tex]
- For 150 tortillas:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 150 = 1250 \][/tex]
- For 200 tortillas:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 200 = 1500 \][/tex]
- For 250 tortillas:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 250 = 1750 \][/tex]

Here is the table representing Chloe's expenses:

| Number of tortillas | 0 | 50 | 100 | 150 | 200 | 250 |
|---------------------|-----|-----|-----|-----|-----|------|
| Total Expenses (R) | 500 | 750 | 1000 | 1250 | 1500 | 1750 |

### 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 draw the graph, plot the points provided in the table and join them with a straight line for both income and expenses.

For total income:

| Number of tortillas | 0 | 50 | 100 | 150 | 200 | 250 |
|---------------------|---|-----|-----|-----|-----|------|
| Total Income (R) | 0 | 750 | 1500 | 2250 | 3000 | 3750 |

For total expenses, use the table as calculated in 1.1.2.

### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even.
To determine the break-even point, set the total income equal to the total expenses:
[tex]\[ \text{Total Income} = \text{Total Expenses} \][/tex]
Using our formulas,
[tex]\[ 15 \times \text{Number of Tortillas} = 500 + 5 \times \text{Number of Tortillas} \][/tex]
[tex]\[ 15T = 500 + 5T \][/tex]
Subtract 5T from both sides:
[tex]\[ 10T = 500 \][/tex]
Solve for T:
[tex]\[ T = \frac{500}{10} = 50 \][/tex]

So, 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.
Given the sale of 240 tortillas, let's calculate the income, expenses, and profit.

- Income:
[tex]\[ \text{Total Income} = 240 \times 15 = 3600 \][/tex]
- Expenses:
[tex]\[ \text{Total Expenses} = 500 + 5 \times 240 = 500 + 1200 = 1700 \][/tex]
- Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} = 3600 - 1700 = 1900 \][/tex]

Here is the completed income and expense statement:

| | Amount (R) |
|--------|------------|
| Income | |
| Sale of 240 tortillas | 3600 |
| Expenses | |
| Fixed cost | 500 |
| Cost of each tortilla | 1200 |
| Total Expenses | 1700 |
| Profit | 1900 |

This analysis shows that Chloe made a profit of R1900 after selling 240 tortillas.

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