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|l|l|l|l|l|}
\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.

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.

Question

11-08-2024
Mathematics

Answered

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|l|l|l|l|l|}
\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.

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.

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-08-11T10:41:41-04:00

Sure! 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
Chloe incurs a fixed cost of R500 for renting the stall, and it costs her R5 to make each tortilla. If we let [tex]$ n $[/tex] represent the number of tortillas sold, the total expenses [tex]$ E $[/tex] can be expressed as:
[tex]\[ E = 500 + 5n \][/tex]

### 1.1.2 Draw Up a Table to Represent Chloe's Expenses
We calculate the expenses based on the formula [tex]$ E = 500 + 5n $[/tex] for the provided number of tortillas ([tex]$ n $[/tex]).

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

### 1.1.3 Draw Line Graphs of Chloe's Total Income and Expenses
For the table values:
- Income: [tex]$ I = 15n $[/tex]
- Expenses: [tex]$ E = 500 + 5n $[/tex]

When converted into tabular format:

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

Graphically, you will plot:
- Income line: [tex]$ (0, 0), (50, 750), (100, 1500), (150, 2250), (200, 3000), (250, 3750) $[/tex]
- Expenses line: [tex]$ (0, 500), (50, 750), (100, 1000), (150, 1250), (200, 1500), (250, 1750) $[/tex]

### 1.1.4 Determine the Minimum Number of Tortillas to Break Even
To find the break-even point, we need to determine when total income equals total expenses. From the table, we observe:
- At [tex]$ n = 50 $[/tex]:
- Income: [tex]$ R750 $[/tex]
- Expenses: [tex]$ R750 $[/tex]

Therefore, the minimum number of tortillas Chloe must sell to break even is [tex]$ \boxed{50} $[/tex]. This is the point at which her income equals her expenses (R750).