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1.1.4 Is the graph an example of direct or indirect proportion? Justify your answer.
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1.1.5 Name the dependent and the independent variables.

1.2 The students are going to charge R50 per car. The table below represents the income.

\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
Number of cars & 0 & 10 & 20 & 30 & A & 60 \\
\hline
Income & 0 & 500 & B & 1500 & 2500 & 3000 \\
\hline
\end{tabular}

1.2.1 Calculate the values for [tex]$A$[/tex] and [tex]$B$[/tex] by writing only the answer next to the letter (A-B) in the ANSWER BOOK.
FORMULA: Income = R50 × number of cars
(2 × 2)

1.2.2 Use the table to draw a straight-line graph on ANSWER SHEET A (attached). Supply a heading and labels for the graph.

1.2.3 What is the maximum income the students can make on one Saturday if they wash 60 cars?
(1)

1.2.4 The students need to raise R10,000.
How many cars do they need to wash to reach their target income?

1.2.5 Will three Saturdays of car washing be enough for the students to reach their target of R10,000? Show all calculations.

1.2.6 Give one suggestion as to how the students can reach their goal of raising R10,000 by washing cars in a shorter space of time.
(1)



Answer :

GinnyAnswer
Sure, let's go through each part step-by-step:

### 1.1.4 Is the graph an example of direct or indirect proportion? Justify your answer.
The graph is an example of direct proportion. This is justified by the fact that the income increases consistently with the number of cars washed. When the number of cars washed doubles, the income also doubles, which indicates that income and the number of cars washed are directly proportional to one another.

### 1.1.5 Name the dependent and the independent variables.
- Dependent variable: Income
- Independent variable: Number of cars washed

### 1.2.1 Calculate the values for A and B by writing only the answer next to the letter (A-B) in the ANSWER BOOK.
Using the formula [tex]\( \text{Income} = R50 \times \text{number of cars} \)[/tex]:

- For [tex]\( A \)[/tex], when the number of cars is 50:
[tex]\[ A = R50 \times 50 = R2500 \][/tex]

- For [tex]\( B \)[/tex], when the number of cars is 20:
[tex]\[ B = R50 \times 20 = R1000 \][/tex]

### 1.2.2 Use the table to draw a straight-line graph on ANSWER SHEET A. Supply a heading and labels for the graph.
To plot the graph, use the following points from the table:

[tex]\[ \begin{tabular}{|c|c|} \hline \text{Number of Cars} & \text{Income (R)} \\ \hline 0 & 0 \\ 10 & 500 \\ 20 & 1000 \\ 30 & 1500 \\ 50 & 2500 \\ 60 & 3000 \\ \hline \end{tabular} \][/tex]

Heading:
"Income vs Number of Cars Washed"

Axes Labels:
- X-axis: Number of Cars
- Y-axis: Income (R)

### 1.2.3 What is the maximum income the students can make on one Saturday if they wash 60 cars?
The maximum income the students can make on one Saturday if they wash 60 cars:
[tex]\[ \text{Maximum income} = R3000 \][/tex]

### 1.2.4 The students need to raise R10 000. How many cars do they need to wash to reach their target income?
To calculate the number of cars needed to reach a target income of R10,000:
[tex]\[ \text{Number of cars} = \frac{R10\,000}{R50\ \text{per car}} = 200\ \text{cars} \][/tex]

### 1.2.5 Will three Saturdays of car washing be enough for the students to reach their target of R10 000? Show ALL calculations.
The maximum income on one Saturday is R3000. Therefore, the total income over three Saturdays is:
[tex]\[ 3 \times R3000 = R9000 \][/tex]

Since R9000 is less than R10,000, three Saturdays of car washing will not be enough to reach the target.

### 1.2.6 Give ONE suggestion as to how the students can reach their goal of raising R10 000 by washing cars in a shorter space of time.
One suggestion for reaching the goal of R10,000 in a shorter space of time is to increase the per car charge or to wash more cars per day.

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