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]$=\cdots$[/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.



Answer :

### Solution

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

To find Chloe's total expenses, you need to account for the cost of making the tortillas and the cost of renting the stall.

- The cost to make each tortilla is R5.
- The stall rent is R500.
- Let [tex]\( n \)[/tex] represent the number of tortillas sold.

The formula for total expenses (E) can be expressed as:
[tex]\[ \text{Total Expenses} = \text{(cost per tortilla} \times \text{number of tortillas)} + \text{stall rent} \][/tex]
[tex]\[ E = (5 \times n) + 500 \][/tex]

So, the formula for Chloe's total expenses is:
[tex]\[ \boxed{E = 5n + 500} \][/tex]

1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas:

Now we calculate the total expenses for each given number of tortillas sold using the formula [tex]\(E = 5n + 500\)[/tex].

1. For 0 tortillas:
[tex]\[ E = 5 \times 0 + 500 = 500 \][/tex]
Total Expenses: R500

2. For 50 tortillas:
[tex]\[ E = 5 \times 50 + 500 = 250 + 500 = 750 \][/tex]
Total Expenses: R750

3. For 100 tortillas:
[tex]\[ E = 5 \times 100 + 500 = 500 + 500 = 1000 \][/tex]
Total Expenses: R1000

4. For 150 tortillas:
[tex]\[ E = 5 \times 150 + 500 = 750 + 500 = 1250 \][/tex]
Total Expenses: R1250

5. For 200 tortillas:
[tex]\[ E = 5 \times 200 + 500 = 1000 + 500 = 1500 \][/tex]
Total Expenses: R1500

6. For 250 tortillas:
[tex]\[ E = 5 \times 250 + 500 = 1250 + 500 = 1750 \][/tex]
Total Expenses: R1750

Let's summarize these results in a table:

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

Thus, Chloe's total expenses for selling varying numbers of tortillas are provided in the table above.