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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 [tex]$R$[/tex]. 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 & [tex]$t$[/tex] & 50 & 100 & 150 & 200 & 250 \\
\hline
Income [tex]$R$[/tex] & 15 & 750 & 1500 & 2250 & 3000 & 3750 \\
\hline
\end{tabular}

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

2. Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 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
To start, let's formulate Chloe's total expenses. Given that it costs R5 to make one tortilla and an additional R500 to rent the stall, we can represent her total expenses mathematically as follows:

Total Expenses = (Cost per tortilla × Number of tortillas) + Stall rental cost
Total Expenses = (5 × t) + 500

Next, we need to calculate Chloe's total expenses for selling 0, 50, 100, 150, 200, and 250 tortillas. By substituting these values of t (number of tortillas) into the expenses formula:

- If Chloe sells 0 tortillas:
Total Expenses = (5 × 0) + 500 = 500

- If Chloe sells 50 tortillas:
Total Expenses = (5 × 50) + 500 = 750

- If Chloe sells 100 tortillas:
Total Expenses = (5 × 100) + 500 = 1000

- If Chloe sells 150 tortillas:
Total Expenses = (5 × 150) + 500 = 1250

- If Chloe sells 200 tortillas:
Total Expenses = (5 × 200) + 500 = 1500

- If Chloe sells 250 tortillas:
Total Expenses = (5 × 250) + 500 = 1750

These calculations give us the following table of expenses corresponding to the number of tortillas sold:

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Number of tortillas & 0 & 50 & 100 & 150 & 200 & 250 \\
\hline
Expenses (R) & 500 & 750 & 1000 & 1250 & 1500 & 1750 \\
\hline
\end{tabular}

Using the income and expenses calculated above, the income and expenses can be represented as follows:

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Number of tortillas & 0 & 50 & 100 & 150 & 200 & 250 \\
\hline
Income (R) & 0 & 750 & 1500 & 2250 & 3000 & 3750 \\
\hline
Expenses (R) & 500 & 750 & 1000 & 1250 & 1500 & 1750 \\
\hline
\end{tabular}

To represent this information graphically, plot the data points on a set of axes for both income and expenses:
- Income: (0,0), (50,750), (100,1500), (150,2250), (200,3000), (250,3750)
- Expenses: (0,500), (50,750), (100,1000), (150,1250), (200,1500), (250,1750)

The points should be connected to form two linear graphs.

Finally, to determine the minimum number of tortillas Chloe must sell in order to break even, compare the income and expenses:

From the values given:
[tex]\( \text{For 50 tortillas:} \)[/tex] Income = R750 and Expenses = R750

Chloe breaks even by selling exactly 50 tortillas because her income equals her expenses (R750) at this point.

Therefore, the minimum number of tortillas that Chloe must sell in order to break even is 50.

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