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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|l|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]\[ \text{Total Expenses} = \cdots \][/tex]

1.1.2 Draw up a table to represent Chloe's expenses if she sells [tex]\(0, 50, 100, 150, 200, \)[/tex] and [tex]\(250\)[/tex] tortillas.

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.



Answer :

GinnyAnswer
Let's go through each part of the given question step-by-step.

### Question 1.1.1

Chloe's total expenses can be broken down into two main components:
- The cost to make each tortilla.
- The fixed cost to rent the stall.

Given:
- The cost to make one tortilla is R5.
- The stall rent is R500.

Let's denote:
- Let [tex]\( x \)[/tex] be the number of tortillas sold.

The total cost to make tortillas would then be [tex]\( 5x \)[/tex] Rands.

The total expenses formula will be the sum of the cost to make the tortillas and the stall rent.

So, the total expenses formula is:
[tex]\[ \text{Total Expenses} = 5x + 500 \][/tex]

### Question 1.1.2

Next, we need to draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas.

Using the formula [tex]\( \text{Total Expenses} = 5x + 500 \)[/tex]:

1. When [tex]\( x = 0 \)[/tex]:
[tex]\[ \text{Total Expenses} = 5(0) + 500 = 500 \][/tex]

2. When [tex]\( x = 50 \)[/tex]:
[tex]\[ \text{Total Expenses} = 5(50) + 500 = 250 + 500 = 750 \][/tex]

3. When [tex]\( x = 100 \)[/tex]:
[tex]\[ \text{Total Expenses} = 5(100) + 500 = 500 + 500 = 1000 \][/tex]

4. When [tex]\( x = 150 \)[/tex]:
[tex]\[ \text{Total Expenses} = 5(150) + 500 = 750 + 500 = 1250 \][/tex]

5. When [tex]\( x = 200 \)[/tex]:
[tex]\[ \text{Total Expenses} = 5(200) + 500 = 1000 + 500 = 1500 \][/tex]

6. When [tex]\( x = 250 \)[/tex]:
[tex]\[ \text{Total Expenses} = 5(250) + 500 = 1250 + 500 = 1750 \][/tex]

So the table representing Chloe's expenses is as follows:
[tex]\[ \begin{array}{|l|l|l|l|l|l|l|} \hline \text{Number of Tortillas} & 0 & 50 & 100 & 150 & 200 & 250 \\ \hline \text{Total Expenses (R)} & 500 & 750 & 1000 & 1250 & 1500 & 1750 \\ \hline \end{array} \][/tex]

### Question 1.1.3

For this part, we use the income data provided in the question and the expenses data we have calculated:

[tex]\[ \begin{array}{|l|l|l|l|l|l|l|} \hline \text{Number of Tortillas} & 0 & 50 & 100 & 150 & 200 & 250 \\ \hline \text{Total Income (R)} & 0 & 750 & 1500 & 2250 & 3000 & 3750 \\ \hline \text{Total Expenses (R)} & 500 & 750 & 1000 & 1250 & 1500 & 1750 \\ \hline \end{array} \][/tex]

To visualize these values, you would plot:

- A line representing total income with coordinates (number of tortillas, total income): (0,0), (50,750), (100,1500), (150,2250), (200,3000), (250,3750).
- Another line representing total expenses with coordinates (number of tortillas, total expenses): (0,500), (50,750), (100,1000), (150,1250), (200,1500), (250,1750).

The x-axis represents the number of tortillas sold, and the y-axis represents the total amount in Rands. The graph will show two lines:
- The total income line rises steeply due to the income per tortilla being R15.
- The total expenses line also rises but at a slower rate due to the combined cost of making tortillas and the fixed stall rent.

By comparing these two lines on the graph, you will be able to see how the expenses and income change with the number of tortillas sold.

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