Test Your Understanding

1. A labor law company charges their clients a fixed monthly fee of R1,200 (called a retainer), plus R400 per hour consultation fee as and when required.

1.1 Complete the table below:

[tex]
\[
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
Number of hours & 0 & 1 & 2 & 3 & C & 9 \\
\hline
Total charge (R) & A & 1600 & 2000 & B & 3600 & 4800 \\
\hline
\end{tabular}
\]
[/tex]

1.2 Determine a formula to represent the relationship between the number of hours and the total charge.

1.3 Use your formula from Question 1.2 to determine:

- 1.3.1 The total charge if a client required their services for 20 hours in a month.
- 1.3.2 The number of hours the labor law company worked for if the total charge was R19,200 for the month.

1.4 Use the completed table from Question 1.1 to draw the graph of the total charges of the labor law company.

2. Cindy hires a seamstress to sew bibs for her. She pays the seamstress R100 per day, plus R25 for each bib she completes.

2.1 Construct a table to represent the seamstress' total pay if she completes 15 bibs in a day.

2.2 Determine a formula to represent the seamstress' total pay.

2.3 Use your table from Question 2.1 to draw the graph of the seamstress' total pay.

2.4 Use your graph from Question 2.3 to determine:

- 2.4.1 How much the seamstress would be paid if she sewed 8 bibs?
- 2.4.2 How many bibs did the seamstress sew if she was paid R450?

Sure, let's work through the problem step-by-step:

### Part 1: Labour Law Company Charges

1.1 Complete the Table:

Given:
- Fixed monthly retainer = R1,200
- Consultation fee = R400 per hour

To find the total charge, we use the formula:
[tex]\[ \text{Total Charge} = 1200 + 400 \times (\text{Number of Hours}) \][/tex]

- For 0 hours:
[tex]\[ A = 1200 + 400 \times 0 = 1200 \][/tex]

- For 3 hours:
[tex]\[ B = 1200 + 400 \times 3 = 2400 \][/tex]

- For a total charge of R3,600:
[tex]\[ 3600 = 1200 + 400 \times C \][/tex]
Rearrange to find [tex]\( C \)[/tex]:
[tex]\[ C = \frac{3600 - 1200}{400} = 6 \][/tex]

So 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 Determine a Formula:

The relationship between the number of hours and the total charge is given by:
[tex]\[ \text{Total Charge} = 1200 + 400 \times (\text{Number of Hours}) \][/tex]

1.3 Using the Formula:

1.3.1 Total Charge for 20 hours:

Plug 20 hours into the formula:
[tex]\[ \text{Total Charge} = 1200 + 400 \times 20 = 9200 \][/tex]

1.3.2 Determining Number of Hours for a Total Charge of R19,200:

Set up the equation:
[tex]\[ 19200 = 1200 + 400 \times (\text{Number of Hours}) \][/tex]
Solve for the number of hours:
[tex]\[ \text{Number of Hours} = \frac{19200 - 1200}{400} = 45 \][/tex]

1.4 Graphing:

Using the completed table from 1.1, you can plot the number of hours on the x-axis and the total charge on the y-axis to create a linear graph showing how total charges increase with more hours.

### Part 2: Cindy's Seamstress

2.1 Table for Seamstress' Total Pay (15 bibs):

- Daily pay = R100
- Pay per bib = R25

To determine total pay for 15 bibs:
[tex]\[ \text{Total Pay} = 100 + 25 \times 15 = 475 \][/tex]

2.2 Determine a Formula:

The formula for the seamstress' total pay, given the number of bibs completed, is:
[tex]\[ \text{Total Pay} = 100 + 25 \times (\text{Number of Bibs}) \][/tex]

2.3 Graphing:

To create a graph, plot the number of bibs on the x-axis and the total pay on the y-axis, using the formula from 2.2.

2.4 Using the Graph:

2.4.1 Total Pay for 8 Bibs:

Using the formula:
[tex]\[ \text{Total Pay} = 100 + 25 \times 8 = 300 \][/tex]

2.4.2 Number of Bibs for R450 Payment:

Set up the equation:
[tex]\[ 450 = 100 + 25 \times (\text{Number of Bibs}) \][/tex]
Solve for the number of bibs:
[tex]\[ \text{Number of Bibs} = \frac{450 - 100}{25} = 14 \][/tex]

This step-by-step breakdown should help you understand how to solve such problems using the given information and formulas.