Sure, let's tackle each question step by step.
### 1.1.1 Define the term income.
Income is the money received for performing a service or selling goods. In this context, income refers to the money Kevin receives for washing cars.
### 1.1.2 Complete the following formula to calculate the income received per car washed.
To calculate the income received per car washed, you use the formula:
[tex]\[ \text{Income (in Rand)} = \text{Number of cars washed} \times \text{Income per car} \][/tex]
Here, the income per car stays constant.
### 1.3 Is this an example of direct or indirect proportion? Explain your answer.
This is an example of direct proportion. In direct proportion, as one quantity increases, the other quantity increases at a constant rate. Here, the income increases directly in proportion to the number of cars washed.
### 1.4 Calculate the missing values of A and B in the table.
To find the missing values [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we'll use the known values in the table and the fact that the income per car is constant.
First, we calculate the income per car. From the table, in June, Kevin washed 11 cars and earned 495 Rand.
[tex]\[
\text{Income per car} = \frac{\text{Total income}}{\text{Number of cars}} = \frac{495}{11} = 45 \text{ Rand per car}
\][/tex]
Now, let's find [tex]\(A\)[/tex]:
- Given that the income in August is 1170 Rand:
[tex]\[
A = \frac{1170}{45} = 26 \text{ cars}
\][/tex]
Next, let's determine [tex]\(B\)[/tex]:
- Given that the number of cars washed in October is 20:
[tex]\[
B = 20 \times 45 = 900 \text{ Rand}
\][/tex]
So, [tex]\(A = 26\)[/tex] and [tex]\(B = 900\)[/tex].
### 1.5 Calculate his total income from June to November.
To calculate the total income, sum up all the monthly incomes:
[tex]\[
\text{Total income} = 495 + 765 + 1170 + 1485 + 900 + 1260 = 6075 \text{ Rand}
\][/tex]
### Summary
1. Income is the money received for performing a service.
2. The formula to calculate income received per car washed is:
[tex]\[
\text{Income (in Rand)} = \text{Number of cars washed} \times \text{Income per car}
\][/tex]
3. This is an example of direct proportion since the income increases as the number of cars washed increases.
4. The missing values are:
- [tex]\(A = 26\)[/tex]
- [tex]\(B = 900\)[/tex]
5. Kevin’s total income from June to November is 6075 Rand.
