Answered

### Worked Example 2

The following is the income and expenditure statement for Ally's Boutique for a specific month:

\begin{tabular}{|l|l|l|l|l|l|}
\hline
\multicolumn{4}{|c|}{\textbf{EXPENDITURE}} & \multicolumn{2}{|c|}{\textbf{INCOME}} \\
\hline
\textbf{OPERATING COSTS} & \textbf{PRODUCTION COST} & & & \textbf{Dresses made} & R60 000,00 \\
\hline
Rental & R5000,00 & Fabric used & R25000,00 & & R3 850,00 \\
Electricity & R450,00 & Other material used & R10 000,00 & & \\
Water & R120,00 & Fittings & & & \\
Telephone and internet & R900,00 & Seamstress wage & \textbf{E} & & \\
\hline
\textbf{Total} & R6470 & \textbf{Total} & R42550 & \textbf{Total} & \\
\hline
\end{tabular}

Source: adapted from grade 12 Math Lit revision workbook

Use the information above to answer the questions that follow.

2.1 Calculate the value of [tex]$E$[/tex].



Answer :

GinnyAnswer
To find the value of [tex]\( E \)[/tex] (the seamstress wage), follow these steps:

### Step-by-Step Solution:

1. List all the known operating costs and their total:
- Rental: R5000
- Electricity: R450
- Water: R120
- Telephone and internet: R900

The total of the known operating costs is [tex]\( R6470 \)[/tex].

2. List all the known production costs:
- Fabric used: R25000
- Other material used: R10000

The sum of these production costs is [tex]\( R25000 + R10000 = R35000 \)[/tex].

3. Find the total production cost given in the problem:
- The total production cost is [tex]\( R42550 \)[/tex].

4. Calculate the seamstress wage [tex]\( E \)[/tex]:
- The total production cost [tex]\( R42550 \)[/tex] is the sum of known production costs and the seamstress wage.

Hence, we can set up the equation:
[tex]\[ R42550 = R35000 + E \][/tex]

5. Solve for [tex]\( E \)[/tex]:
- Subtract the known production costs from the total production cost:
[tex]\[ E = R42550 - R35000 \][/tex]

6. Calculate the result:
[tex]\[ E = R7550 \][/tex]

Therefore, the value of [tex]\( E \)[/tex] is [tex]\( R7550 \)[/tex].

### Verification
To ensure the accuracy, let’s verify the total operating costs:
- Known operating costs are [tex]\( R5000 + R450 + R120 + R900 = R6470 \)[/tex].

It confirms that the total operating costs are correct as per the given data. Thus, the calculated seamstress wage [tex]\( E \)[/tex] is accurate.

Final Answer:
The value of [tex]\( E \)[/tex] is [tex]\( \boxed{R7550} \)[/tex].