Answer :
Sure, let's solve the questions step-by-step:
### Question 1
1.1 Complete the table
The formula to calculate the total charge by the labour law company is as follows:
[tex]\[ \text{Total Charge} = \text{Retainer} + (\text{Hourly Fee} \times \text{Number of hours}) \][/tex]
where the Retainer is R1,200 and the Hourly Fee is R400.
Given:
- Number of hours = 0:
[tex]\(\text{Total Charge} = 1200 + (400 \times 0) = 1200\)[/tex]
Therefore, A = 1200.
- Number of hours = 3:
[tex]\(\text{Total Charge} = 1200 + (400 \times 3) = 2400\)[/tex]
Therefore, B = 2400.
- For a Total Charge of R3600,
[tex]\(3600 = 1200 + (400 \times \text{C})\)[/tex]
Solving for C, [tex]\(\text{C} = \frac{3600 - 1200}{400} = 6\)[/tex].
The completed table is:
[tex]\[
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
Number of hours & 0 & 1 & 2 & 3 & 6 & 9 \\
\hline
Total charge (R) & 1200 & 1600 & 2000 & 2400 & 3600 & 4800 \\
\hline
\end{tabular}
\][/tex]
1.2 Formula to represent the relationship
The formula is:
[tex]\[ \text{Total Charge} = 1200 + 400 \times \text{Number of hours} \][/tex]
1.3 Use the formula
1.3.1 Total charge if a client required their services for 20 hours:
[tex]\[ \text{Total Charge} = 1200 + 400 \times 20 = 9200 \][/tex]
So, the total charge is R9,200.
1.3.2 Number of hours if the total charge was R19,200:
[tex]\[ 19200 = 1200 + 400 \times \text{Number of hours} \][/tex]
Solving for the number of hours:
[tex]\[ \text{Number of hours} = \frac{19200 - 1200}{400} = 45 \][/tex]
1.4 Graph the completed table
Using the completed table, plot the number of hours on the x-axis and the total charge on the y-axis. Connect the points to form a straight line, showing the linear relationship between the number of hours and the total charge.
### Question 2
2.1 Construct a table for 15 bibs
The formula for the seamstress' total pay is:
[tex]\[ \text{Total Pay} = \text{Daily Fee} + (\text{Per Bib Fee} \times \text{Number of Bibs}) \][/tex]
where the Daily Fee is R100 and the Per Bib Fee is R25.
For 15 bibs:
[tex]\[ \text{Total Pay} = 100 + 25 \times 15 = 475 \][/tex]
The table entry would be:
Number of bibs = 15, Total Pay = R475.
2.2 Formula to represent the seamstress' total pay
The formula is:
[tex]\[ \text{Total Pay} = 100 + 25 \times \text{Number of Bibs} \][/tex]
2.3 Graph the table
Using the table (similar to 2.1) plot the number of bibs on the x-axis and the total pay on the y-axis. Connect the dots to form a graph, showing the linear relationship.
2.4 Use the graph
2.4.1 Pay for sewing 8 bibs:
[tex]\[ \text{Total Pay} = 100 + 25 \times 8 = 300 \][/tex]
The seamstress is paid R300.
2.4.2 Number of bibs if paid R450:
[tex]\[ 450 = 100 + 25 \times \text{Number of Bibs} \][/tex]
Solving for the number of bibs:
[tex]\[ \text{Number of Bibs} = \frac{450 - 100}{25} = 14 \][/tex]
This concludes the detailed step-by-step solution for the given questions.
### Question 1
1.1 Complete the table
The formula to calculate the total charge by the labour law company is as follows:
[tex]\[ \text{Total Charge} = \text{Retainer} + (\text{Hourly Fee} \times \text{Number of hours}) \][/tex]
where the Retainer is R1,200 and the Hourly Fee is R400.
Given:
- Number of hours = 0:
[tex]\(\text{Total Charge} = 1200 + (400 \times 0) = 1200\)[/tex]
Therefore, A = 1200.
- Number of hours = 3:
[tex]\(\text{Total Charge} = 1200 + (400 \times 3) = 2400\)[/tex]
Therefore, B = 2400.
- For a Total Charge of R3600,
[tex]\(3600 = 1200 + (400 \times \text{C})\)[/tex]
Solving for C, [tex]\(\text{C} = \frac{3600 - 1200}{400} = 6\)[/tex].
The completed table is:
[tex]\[
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
Number of hours & 0 & 1 & 2 & 3 & 6 & 9 \\
\hline
Total charge (R) & 1200 & 1600 & 2000 & 2400 & 3600 & 4800 \\
\hline
\end{tabular}
\][/tex]
1.2 Formula to represent the relationship
The formula is:
[tex]\[ \text{Total Charge} = 1200 + 400 \times \text{Number of hours} \][/tex]
1.3 Use the formula
1.3.1 Total charge if a client required their services for 20 hours:
[tex]\[ \text{Total Charge} = 1200 + 400 \times 20 = 9200 \][/tex]
So, the total charge is R9,200.
1.3.2 Number of hours if the total charge was R19,200:
[tex]\[ 19200 = 1200 + 400 \times \text{Number of hours} \][/tex]
Solving for the number of hours:
[tex]\[ \text{Number of hours} = \frac{19200 - 1200}{400} = 45 \][/tex]
1.4 Graph the completed table
Using the completed table, plot the number of hours on the x-axis and the total charge on the y-axis. Connect the points to form a straight line, showing the linear relationship between the number of hours and the total charge.
### Question 2
2.1 Construct a table for 15 bibs
The formula for the seamstress' total pay is:
[tex]\[ \text{Total Pay} = \text{Daily Fee} + (\text{Per Bib Fee} \times \text{Number of Bibs}) \][/tex]
where the Daily Fee is R100 and the Per Bib Fee is R25.
For 15 bibs:
[tex]\[ \text{Total Pay} = 100 + 25 \times 15 = 475 \][/tex]
The table entry would be:
Number of bibs = 15, Total Pay = R475.
2.2 Formula to represent the seamstress' total pay
The formula is:
[tex]\[ \text{Total Pay} = 100 + 25 \times \text{Number of Bibs} \][/tex]
2.3 Graph the table
Using the table (similar to 2.1) plot the number of bibs on the x-axis and the total pay on the y-axis. Connect the dots to form a graph, showing the linear relationship.
2.4 Use the graph
2.4.1 Pay for sewing 8 bibs:
[tex]\[ \text{Total Pay} = 100 + 25 \times 8 = 300 \][/tex]
The seamstress is paid R300.
2.4.2 Number of bibs if paid R450:
[tex]\[ 450 = 100 + 25 \times \text{Number of Bibs} \][/tex]
Solving for the number of bibs:
[tex]\[ \text{Number of Bibs} = \frac{450 - 100}{25} = 14 \][/tex]
This concludes the detailed step-by-step solution for the given questions.
