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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:
[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. Write down a formula to represent Chloe's total expenses:
Total Expenses [tex]\( = \cdots \)[/tex]

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.

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.

4. Determine the minimum number of tortillas that Chloe must sell in order to break even.



Answer :

GinnyAnswer
Sure, let's go through the solution step-by-step.

### 1.1.1 Formula to Represent Chloe's Total Expenses

First, we need to determine the formula for Chloe's total expenses. She incurs a cost for each tortilla she makes and also has to pay a fixed rental cost for her stall.

- The cost to make one tortilla is R5.
- The fixed rental cost is R500.

If we let [tex]\( x \)[/tex] represent the number of tortillas Chloe makes and sells, the total expense [tex]\( E(x) \)[/tex] can be represented by the following formula:
[tex]\[ \text{Total Expenses} = (5 \times \text{number of tortillas}) + 500 \][/tex]
So, in formulaic terms:
[tex]\[ \text{Total Expenses} = 5x + 500 \][/tex]

### 1.1.2 Table Representing Chloe's Expenses

Next, we need to calculate the total expenses for different numbers of tortillas sold: 0, 50, 100, 150, 200, and 250.

Let's compute the expenses:

- For 0 tortillas:
[tex]\[ 5 \times 0 + 500 = 500 \][/tex]
- For 50 tortillas:
[tex]\[ 5 \times 50 + 500 = 250 + 500 = 750 \][/tex]
- For 100 tortillas:
[tex]\[ 5 \times 100 + 500 = 500 + 500 = 1000 \][/tex]
- For 150 tortillas:
[tex]\[ 5 \times 150 + 500 = 750 + 500 = 1250 \][/tex]
- For 200 tortillas:
[tex]\[ 5 \times 200 + 500 = 1000 + 500 = 1500 \][/tex]
- For 250 tortillas:
[tex]\[ 5 \times 250 + 500 = 1250 + 500 = 1750 \][/tex]

The table of expenses would look like this:

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|} \hline \text{Number of tortillas} & 0 & 50 & 100 & 150 & 200 & 250 \\ \hline \text{Total Expenses (R)} & 500 & 750 & 1000 & 1250 & 1500 & 1750 \\ \hline \end{array} \][/tex]

### 1.1.3 Line Graph of Income and Expenses

To create a line graph, you would need to plot the data points for both total income and total expenses on the same set of axes.

For Total Income:
- For 0 tortillas: 0
- For 50 tortillas: 750
- For 100 tortillas: 1500
- For 150 tortillas: 2250
- For 200 tortillas: 3000
- For 250 tortillas: 3750

For Total Expenses:
- For 0 tortillas: 500
- For 50 tortillas: 750
- For 100 tortillas: 1000
- For 150 tortillas: 1250
- For 200 tortillas: 1500
- For 250 tortillas: 1750

### 1.1.4 Minimum Number of Tortillas to Break Even

The break-even point occurs when Chloe's total income equals her total expenses. We need to find the number of tortillas [tex]\( x \)[/tex] for which the total income equals the total expenses.

1. Income per tortilla is R15.
2. Expenses are given by [tex]\( 5x + 500 \)[/tex].

So, at break-even:
[tex]\[ 15x = 5x + 500 \][/tex]
[tex]\[ 15x - 5x = 500 \][/tex]
[tex]\[ 10x = 500 \][/tex]
[tex]\[ x = \frac{500}{10} \][/tex]
[tex]\[ x = 50 \][/tex]

Therefore, Chloe needs to sell a minimum of 50 tortillas to break even.