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

1.1.1 Write down a formula to represent Chloe's total expenses:

Total Expenses [tex]$=$[/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.

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

(2)



Answer :

GinnyAnswer
Sure, let's break down the solution step by step:

### 1.1.1 Formula for Chloe's Total Expenses

To determine Chloe's total expenses, you need to account for the cost of making tortillas and the rental cost of the stall. Chloe's cost per tortilla is R5, and the rental cost of the stall is R500.

So, the formula for Chloe's total expenses [tex]\( E \)[/tex] when she sells [tex]\( n \)[/tex] tortillas is:
[tex]\[ \text{Total Expenses} = \text{Rent Cost} + (\text{Cost per Tortilla} \times \text{Number of Tortillas}) \][/tex]
[tex]\[ E = 500 + 5n \][/tex]

### 1.1.2 Expenses Table

Using the formula derived above, we can create a table showing Chloe's total expenses for selling different quantities of tortillas (0, 50, 100, 150, 200, 250):

\begin{tabular}{|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{tabular}

### 1.1.3 Line Graph (Income and Expenses)

Unfortunately, I cannot draw graphs directly here, but I can guide you on how to plot them.

1. Prepare your graph paper or graphing software.
2. Label the axes:
- X-axis: Number of Tortillas (0, 50, 100, 150, 200, 250)
- Y-axis: Amount in Rands (0 to 3750)
3. Plot the points for total income:
- 0 tortillas: R0
- 50 tortillas: R750
- 100 tortillas: R1500
- 150 tortillas: R2250
- 200 tortillas: R3000
- 250 tortillas: R3750
4. Connect the income points with a line.
5. Plot the points for total expenses:
- 0 tortillas: R500
- 50 tortillas: R750
- 100 tortillas: R1000
- 150 tortillas: R1250
- 200 tortillas: R1500
- 250 tortillas: R1750
6. Connect the expense points with a line.
7. Make sure to label your graphs accordingly.

### 1.1.4 Break-Even Point

To determine the minimum number of tortillas Chloe needs to sell to break even, you need to find where the total income equals the total expenses.

The break-even point can be found by solving the equation:
[tex]\[ \text{Total Income} = \text{Total Expenses} \][/tex]
[tex]\[ 15n = 500 + 5n \][/tex]

Subtract [tex]\( 5n \)[/tex] from both sides:
[tex]\[ 10n = 500 \][/tex]

Solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{500}{10} \][/tex]
[tex]\[ n = 50 \][/tex]

So, Chloe must sell a minimum of 50 tortillas to break even.

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