Answered

### Question 2

#### 2.1
Paul and Jane decided to hire laborers to help with the making of face shields while they handle administrative and marketing work.

The table below shows the number of laborers needed to finish the job and the number of days it will take them to do so.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Number of Laborers & 1 & 2 & 3 & 5 & 10 & C \\
\hline
Number of Days & 30 & 15 & 10 & A & B & 2 \\
\hline
\end{tabular}

#### 2.1.1
Determine the values of [tex]$A$[/tex], [tex]$B$[/tex], and [tex]$C$[/tex] in the table above. Write down [tex]$A$[/tex], [tex]$B$[/tex], and [tex]$C$[/tex] in your answer book together with the calculated answers.

#### 2.1.2
What type of relationship does the table represent? (6) (2)

#### 2.1.3
Which one of the following formulas is correct? Choose the answer and write only the letter (A-D) next to the question number (2.1.3) in the ANSWER BOOK.

A. Number of days [tex]$\times$[/tex] number of laborers [tex]$= 30$[/tex]

B. Number of days [tex]$= 30 \times$[/tex] number of laborers

C. Number of days [tex]$\div$[/tex] number of laborers [tex]$= 30$[/tex]

D. Number of laborers [tex]$\div 30 =$[/tex] number of days

#### 2.1.4
Use the table in QUESTION 2.1 to draw and label a graph on ANSWER SHEET 1 (attached) that shows the number of laborers against the number of days taken to finish the job. Label both the horizontal and vertical axes and provide a suitable heading for the graph.

[tex]\[ [20] \][/tex]



Answer :

GinnyAnswer
Let's break down each part of the question step-by-step:

### 2.1.1 Determine the values of [tex]\( A, B \& C \)[/tex]

Given the data:
- When 1 laborer works, it takes 30 days.
- When 2 laborers work, it takes 15 days.
- When 3 laborers work, it takes 10 days.
- When 5 laborers work, it takes [tex]\( A \)[/tex] days.
- When 10 laborers work, it takes [tex]\( B \)[/tex] days.
- When [tex]\( C \)[/tex] laborers work, it takes 2 days.

To find [tex]\( A \)[/tex]:
- From the pattern, we realize that the relationship between the number of laborers and the number of days is inversely proportional: [tex]\( \text{Number of laborers} \times \text{Number of days} = \text{constant} \)[/tex].
- For 1 laborer working 30 days, the constant = 1 × 30 = 30.
- Therefore, for 5 laborers, the number of days [tex]\( A \)[/tex] can be found using [tex]\( 5 \times A = 30 \)[/tex].
- Solving for [tex]\( A \)[/tex]: [tex]\( A = 30 / 5 = 6 \)[/tex] days.

To find [tex]\( B \)[/tex]:
- Similarly, for 10 laborers, [tex]\( 10 \times B = 30 \)[/tex].
- Solving for [tex]\( B \)[/tex]: [tex]\( B = 30 / 10 = 3 \)[/tex] days.

To find [tex]\( C \)[/tex]:
- [tex]\( C \)[/tex] laborers take 2 days to finish the job. Using the constant:
- [tex]\( C \times 2 = 30 \)[/tex].
- Solving for [tex]\( C \)[/tex]: [tex]\( C = 30 / 2 = 15 \)[/tex] laborers.

Thus, the values are:
- [tex]\( A = 6 \)[/tex]
- [tex]\( B = 3 \)[/tex]
- [tex]\( C = 15 \)[/tex]

### 2.1.2 Type of Relationship
The table represents an inversely proportional relationship. As the number of laborers increases, the number of days to finish the job decreases proportionally.

### 2.1.3 Correct Formula Choice
The correct formula to represent the relationship is:
- A. Number of laborers * Number of days = 30

### 2.1.4 Drawing the Graph
You are required to draw and label a graph based on the provided table. Here is a description of how you should plot the graph:

- Horizonal Axis (x-axis): Number of Laborers
- Vertical Axis (y-axis): Number of Days
- Title: Relationship between Number of Laborers and Number of Days to Finish the Job

Points to Plot:
- (1, 30)
- (2, 15)
- (3, 10)
- (5, 6)
- (10, 3)
- (15, 2)

The graph will illustrate that as the number of laborers increases, the number of days decreases, reflecting an inversely proportional relationship.

By following these steps, you can accurately address each part of Question 2.1.